They cost a lot so they do deserve the FG42 by default. It is like saying, Oh, give Shocktroops all bolts actions, make them have upgrade to PPSH.
I think they are fine the way they currently are. They are 4 models only. They drops like flies similarly to Pzgrens when vet 0 or so. They need to vet in order to become durable. I think it is ok the way it is.
They have utility costing ammo. I think it would be utterly ridiculous if they had on top, costing for a weapon upgrade.
Paratroopers, which are pretty directly comparable to falls as they're anti infantry specialists, cost a lot too and they don't get weapons for free. Heck, so do obers.
Paratroopers are also super squishy in terms of RA but are 6 men to compensate.
I take bigger issue with the fact that falls have fausts for some reason. They're the only elite infantry that has any sort of snare and IMO is a bigger incentive for spam than not having to upgrade weapons.