One thing that most XCom player do is hire a bunch of soldiers and keep the few that meet their expectations. This hire and fire mechanic is boring and really adds nothing to the game.
It could entirely be replaced by something where the initial hiring cost of soldiers is higher but soldiers come with better stats. Set your soldiers' hiring cost 5x more and set the stats so that you keep all of them instead of 1 in 5. End result: You paid 5x the hiring cost of vanilla soldiers and you got the number of soldiers you wanted. And you saved yourself the tedium of screening.
Of course, you can't always afford to pay 5x the cost (especially in the early game) so that not entirely equivalent. Also, I think in OpenXCom the hiring cost and monthly costs are the same, so setting hiring cost at 5x means you're paying 5x the monthly costs and that's certainly not equivalent.
Personally, I have a set of statstrings that significantly speed up the screening process and that seems to take care of the useless rookie problem.
There are also plenty of ways to train your useful rookies so that they become decent. Give them the "easy" weapons so they hit aliens easily. Anything explosive is good for that, arcing explosives are the best. Missed the alien by 5 tiles? Who cares, you hit the ground, stuff explodes and you hurt the alien. Since the alien wasn't at ground zero, it survived so now rookie #2 can take a shot too!
Always give them priority in trying to kill aliens too. Your 90+ accuracy sniper sure is awesome, but let the rookies who are scouting take a few shots first (not the guy who just spotted the alien and will take reaction fire to the face though!). With laser weapons it doesn't cost you anything (except making the battle a bit longer) and once in a while, they'll hit and become better, saving your sniper's fire for when you really need it.
Finally, having advanced armors with stat bonuses helps a lot for the rookies too. Veterans need heavy armors because you don't want them to die. They already have awesome stats so they don't need the bonus. Rookies can weak crappier armor that boosts TUs/Reactions/Accuracy, allowing them to do more and thus get more experience. If the rookie gets shot and dies because his armor wasn't heavy enough, who cares? He was a rookie any ways. If he gets enough experience to become valuable, give him a heavier armor. (Or course you could also have heavy armors with stat bonuses, but then it becomes OP armor..).
