The coop scoring system incentivizes player 'racing' to score, and score whoring (to get the most kills or take out single action objectives) -- at the expense of teamwork, and in many cases even at the expense of other players; where racing players run in front of someone trying to cover movement and getting killed or getting the covering player killed unnecessarily.
If this were an infrequent thing it wouldn't be an issue but it's not; there are even servers with messages that try to discourage and even moderate it -- but it wouldn't be a difficult issue to solve or at least ameliorate dramatically as players that support their team, play fair, cover from outside an objective, or cover someone trying to demolish an objective aren't currently rewarded, at all...
One way to approach this would be to reward players that cover outside objectives that execute "x" number of kills, say six or more, or some percentage of the average inside the objective get objective capture points too. This would reward realistic cover and support, more importantly remove the incentive for racing, and incentivize more realistic and complete use of the map.
Similarly rewarding one player for getting to a weapons cache first isn't realistic or even an honest achievement, as it's very easy to game the game and get there first if that's all you want to do. Instead, why not reward every surviving player when the objective was demolished, as all have played some part in getting someone in to demolish an objective...