I remember we've had a thread or two going over the possibility of 2CP Paratroopers. Even made a test mod for it too.
Wasn't the general sentiment that even with their weapons locked behind racks and 6th man behind an upgrade, they were still particularly strong for 2CP?
I made such a thread a long time ago.
A big problem with making paras come earlier (which by all right they should IMO, to make this an actual proper "Airborne" Company) is the weapon upgrades being extremely good. Without them, they're about what one might expect for 380mp call-in infantry squad, CP2 or otherwise. Basically a penal squad notably stronger at close range thanks to 80% accuracy up to almost range 5. Good moving accuracy stats too.
The big reason I wanted them earlier then, of course, besides having to try to fit them into the necessarily infantry-heavy USF build, was because they had 1.0 RA up until vet 3(!) which meant they arrived on the scene having to face vetted infantry that bled them rather terribly until Paras could reach their final veterancy requirements (which will take a very long time to reach with only carbines).
They recently had their starting RA reduced to 0.95, so it's not so much of a problem now.
I do still wish Paras could have their weapon upgrades turned down a bit (4 to 2 thompsons, maybe, taking up only one weapon slot for half the current cost, 1 LMG instead of 2, again for half the current cost, both still cancelling the other out) and then rounding out the base unit a bit, making it more approachable and a bigger part of any airborne build, and allowing for more experimentation with slot item weapons instead of having this unit have the option of one or two mandatory upgrades.
Could then possibly lock their cooked grenade behind grenade tech, but split their RA bonuses between vet levels, or reduce their requirements a bit in general, and then lock weapon upgrades behind either weapon racks or some tech requirement, and then let them come in at CP2. If need be, 6th man could even be something delivered through vet 1, as opposed to any sort of inevitably mandatory upgrade.
After seeing the huge mess the Fallschirmjaeger rework made, however, I'm not sure there's any chance of this stuff happening.