Playing without the kickoff table would suck the soul out of the game. It's bad enough that Cyanide haven't been able to add special play cards as yet.
Comparison with Bridge is problematic - that's a team game, not a solo one, and card random is NOT the same as dice random.
Blood Bowl's roots are in wargaming. It's better to compare it with Warhammer, Flames of War or Bolt Action. And to a degree with real team sports.
Thing with Amazons is that because their replacement players are cheap and effective (especially the Blitzers) the high player loss isn't really that big a deal once you get over the psychological side of that. Claws in particular are just free inducement money to them. One way to counter PO is to invest in Dirty Player/Sneaky Git and make them pay for lying down on the job. Bribes help, as do SPs with chainsaws.
But like all low AV teams, don't get too attached to players.
Another Amazon strength is a starting roster with four Blodgers. They can start picking up support skills immediately. And more importantly, when you need to replace a Blitzer, they have it. Elf Blitzers need a skill up to get it; most other Blodger candidates need two.
Decent passing potential, too.
I tend to go for "receive first" as well. One factor that can affect the decision is weather - generally it's better to let the other guy deal with pickup penalties first. Sweltering Heat is an exception, as the first drive may be the only one where you have 11 on the pitch.
You may also want to take charge against secret weapons, though a cunning player may just leave them in reserve if they kick.
Oh, and they may not be an obvious one, but Orcs can be tuned into a decent passing team. They have a proper Thrower and Goblins can shelter behind tough guys until they're in catch and score range. A +MA or +AG Gobbo is gold. More of a medium range than long range pass strategy, but you can bash and hold really well.
Necromantic are pretty good all round too.
If you want a passing team with more survivability, High Elves are also worth a look. On the other hand, Undead and Necromantic have good receivers and can develop a passing game with a couple of doubles and some team RRs.
Humans are decent. They start with every relevant reroll skill and fast catchers.
Lizards are great, but have no real ability to develop a passer.
Wood Elves are really no more fragile than Skaven and have a better big guy and Wardancers