It's basically a way to offset the risks of going fast vehicle. Fast vehicle leaves you without weapon unlocks (+most likely a muni float as a result) and maybe more rear echelons at the start than are useful in the mid game.
So use thompsons to replace BARs and give you some nice close quarters infantry whilst converting unupgraded REs into something useful. If you're going heavy vehicle then there's no better force to accompany them - you don't have to spend the time hopping the crew in and out as they're already out and accompanying you.
As for veterancy and late game usefulness, I find that I very rarely get my REs to vet 2 and beyond, and rarely spend the munitions giving them weapons that I could give to riflemen. This basically relegates them to capping, repairing and supporting from mid game onwards. A unit of thompson crew can do all this better plus also be able to fight off anything close range. They're relevant mid game at any veterancy and get triple vet extremely quickly at a point where most squads are first or second level vet. Their bonuses are basically the same as Assault engineers who I never think twice about using as a frontline unit with a flame upgrade.
Further into the late game you can see it as an opportunity for an extra 160mp, 100 muni investment to have an assault repair unit every time you get another vehicle out.
This is a very low assesment of REs, and they're actually pretty good, let me explain why:
they are cheap, have 15%(?) better accuracy than Riflemen, componded further with weapon upgrades. They are statted similar to Conscripts, and their vets make them even better. Late game, 3x REs with 2xBARs is a force to be reckoned with, especially if you are charging a position, losses are easily replaced (16 MP) and they can build their own green cover after forcing the enemy out (tank traps. I think the tommy guns are going to be better suited for use by the airborne, not the vehicle crews.