The trick with Fallschirmjagers is that unlike most other elite squads, they're actually a generalist squad (stealth, faust, long-range). So, if we overbuff them in anyway, that's going to be the next panzerfusilier blob.
Specialist short-range squads have to come out stronger than average to allow them to have any effect. Conversely, those elite squads gain significantly reduced bonuses compared to the opposition, simply because they come out stronger than they "should" at Vet0.
For Falls, as long as the bleed is not insane, they can still chip away at enemy squads and gain vet. Perhaps, the question we should ask is whether to further reduce the cost of callin in Fallschirmjagers, or move some of their later vet bonuses to vet0, so that they don't have to wait that long to deal damage (now that they don't have the annoying infiltration mechanic anymore).
About long range - commandos can pick 2 brens and with it they will be stronger on long range then falls. At the same time commandos have stealth too.
In comparison with pantherfusiliers - fusiliers have 6 mens at squad, so its harder to counter with snipers (now snipers in meta like never before due penals spam and t1 soviet meta), and much harder to wipe with mortars/arty/grenade. So spam of the falls are easier to counter then fusilier squad.
To be honest fusilliers look more like base squade (like volks, rifles, cons and other), than like the elite squads (like commandos, soviet stormtroopers and guards, obers and other).
And last moment about vet bonuses - if you lost a vet3 commandos squad in late game (its harder then lost a falls squad due commandos have a 5-mens) you can call a new squad and give them 2 brens to make them usefull against axis vet squads. At the same time if you lost a vet5 falls squad, you cant do anything to make new squad usefull as commandos with brens (and as far as I know falls in current coh2 version need much more exp for vet5 than commandos for vet3).
P.S. I always compare with commandos, because I think that units have the same role on the battlefield - invisible elite squad for flank attacks and wiping hmg/atguns crews.
UPD. About fausts: my idea with FG42 upgrade by 100 muni cost will make impossible to spam them in early/mid game and make impossible to use few pantherfausts in the same time everywhere.