TL;DR Necrons as a faction are in a pitiful state, they are long overdue for buffs and it's in the best interests of game balance, not to mention quality, that Necrons receive fixes ASAP. The faction generally falls behind in all fundamental areas of design and needs significant general buffs to fix it.

Necrons are currently extremely under powered. They suffer from a multitude of weaknesses that combine to absolutely cripple the faction. In the original closed beta, they were extremely strong, arguably borderline however a series of dramatic changes since then has left them completely outclassed by other factions as they have no had any buffs to compensate. In this thread I will list Necron weaknesses, and will provide brief analysis/recommended fixes for the most pressing issues.

Edit: The non-dev balance team (which I occasionally contribute to) is putting together a document with a list of suggestions for game balance, however I wanted to make this post as an individual opinion piece in addition to that.

Biggest issues
Very poor overall mobility/speed
Aside from high armour, they are surprisingly fragile
Extremely lackluster DPS, point for point, compared to other factions fleets

Very poor overall mobility/speed
Aside from their one gimmick, inertialess drive, Necrons are actually extremely slow. While their base speed is slightly high, every other faction has use of other maneuvers (like all full ahead) that provide consistently higher movement, albeit with some micro, that effectively mean they cover much more distance than Necrons over the course of a match.
Inertialess drive has potential to be very strong, but once that 9k jump is used it's on cooldown for a very long time and your ships are completely vulnerable. Necrons are the least capable faction for kiting anything, which is absolutely crucial, especially considering their very low ship count.
Necrons really need a buff to mobility. Even with mass recall they are severely limited. I think some minor buffs to base speed are warranted, as well dramatically reducing the cooldown on inertialess drive, so that Necrons aren't instantly countered by certain fleets, que Massing Nova cannons
Necrons have few ships, so they need to be able to control positioning in other ways, by being decently mobile!

Aside from high armour, they are surprisingly fragile
The HUGE damage reduction given by 83% armour value is not to be overlooked, however it's an overall game issue, not an issue with just Necrons. Aside from this armour value, Necrons are actually quite squishy. Firstly, they completely lack shields, which contribute an enormous amount of raw HP over the course of a battle considering they recharge. Necrons just don't get this, instead they get Hull Cauterization which is objectively terrible, let me provide an example:

A Retribution Battleship touts 2400 hull + 800 shield, the shield, once depleted, recharges within what, 1-2 minutes?
A Cairn Battleship also touts 2400 hull + hull cauterization, so it gets 1 hull point back per second. Now let's say your match lasts 10 minutes (or perhaps longer but the Cairn only lasts 10mins ), at 1 hull point per second, the Cairn would only have an effective 600 more hull over that period and remember the Cairn only starts gaining this additional effective HP once it starts taking damage. So the Cairn has to last in combat 10 minutes (with uninterrupted Hull Cauterization) to even receive that effective HP, which the retribution literally starts the game with. The only redeeming factor here is that Cairns armour comes into play, but this bonus doesn't make up for the flat HP the retribution gets by comparison.
When shield HP was doubled back in the second(?) closed beta, almost every faction got a huge effective buff from this change, Hull Cauterization has remained completely unchanged since then so it's no surprise at all that Necrons now suffer from poor survivability. When armour gets rightfully reverted to it's prior more balanced increments of 25%/50%/75%, Necrons will be even softer!
Proposed fixes:
Firstly, give Necrons more hull! Not a huge buff, but maybe an extra 200 hull on some ships would make a world of difference. Secondly, either buff Hull Cauterization or give a substantial buff to the stance which boosts Hull Cauterization, making reactive hull shift actually worth setting as a stance so it keeps your ships going!
Side note Necrons being so slow are also very vulnerable to ramming, once ramming gets buffed they will need a way to avoid or tank ramming damage. I would also recommend that the bigger a Necrons ship is, the better hull Cauterization should be but it is something you have to be very mathematically careful when buffing. Just my opinion here.

Extremely lackluster DPS, point for point, compared to other factions fleets
Before all shield HP was doubled, Necrons ability to damage enemy fleets was pretty strong. They now have serious trouble agaisnt well shielded factions, however are still somewhat competent agaisnt those without shields, namely Eldar.
Necrons pay huge points for their ships, and this cost isn't entirely unjustified as they do have potential to be strong, and have plenty of utility, however as for their damage, they are horribly over-costed.
Consider this, for a Cairn to actually start dealing hull damage to a Retribution (remember it's particle whip turrets bypass shields), it takes 4 volleys, so exactly 1 whole minute of fire to even touch the enemy hull! That's not great performance.
Now consider that the Cairn's main damage output is limited to 9k, and it can't even fire at anything beyond 13.5k. GOOD LUCK vs ANY LONG RANGED FLEET!
Buffs are needed, however caution must be taken so that Necrons don't stomp Eldar since they perform better agaisnt them than most factions.
Possible improvements are:

• Increase range/damage/rate of fire of Particle whip turrets
• Small decrease in reload time for Lightning arc turrets. Keep range as is.
• Small point cost reductions for Necron weapons
  I think that significant buffs to Particle whip turrets would put Necrons in a nice spot, as they provide good versatile, yet not over the top damage for Necrons fleets which do suffer from a severe lack of flexible/long ranged firepower.

Some other minor things that could use help

• Necrons only have a few viable fleet abilities/upgrades. Consider tweaking so that we don't see the same upgrades every match.
• DOOM SCYTHES ARE SO BAD PLEASE BUFF THEM
• No real reason to use any light cruiser but the shroud?

Obviously if Necrons received all these buffs they might become too strong, but they are in desperate need of some buffs to be even remotely effective. I have quite literally given up on trying to play them until they get some fixes as it;s just not fun entering a match you are almost guaranteed to lose.
Please upvote this so the devs see it and comment if you have anything to add. Thanks for reading.

I agree to the above post. During closed beta the Necrons where OP, but only because of spamming AoE attack after jumping in. That got nerfed, and we are all in agreement about that being a good call. But just like the Lances are currently worthless, the Particle whip is more of a fun gimmick than usefull. Lightning arcs are the only thing usefull, and mostly because of the ability to get shots of to all enemy ships even with 50% less damage still means that the total damage output per salvo is increased if you think about it in "fleet wide" terms. Other than that, the Necrons, which should be a terrifying and slow-but OP faction IF they can close the distance, are anything but. Currently they are just slow and weak.

I think that you forgot to mention that they take critical damage very very easily. Their ships are constantly crippled. A quick kind of solution to this would be to have pyramidal reconstruction as an admiral default ability. I'd actually say that this is even more important than a DPS or HP buff. After this, the second most needed thing in my opinion is the mobility buff.

Yeah the critical chances are what crippled them I find. May as well be a drifting hulk if everything on you is destroyed.

If repairs to their critical components were passive it might be tolerable. Or if they had a better way of actively repairing them. Not having shields means every point of damage can critical you. A passive -%chance to receive criticals night help also

I also find they don’t get to make much use of their Hull Cauterization ability, having to disengage them from combat while they heal up is difficult given their proclivity for having less total vessels.

Maybe we could consider an active ability that shuts the vessel down for rapid regeneration at the same penalty as Hull Cauterization. So you can choose to passively regenerate in combat or disengage and shutdown temporarily to generate more. We could sort out penalties/trade off for the shutdown vessel.