Definitely a popular idea I’ve heard suggested a few times. The primary challenge would be how the developers would make it work. Things also would require some serious rewrites and reconsiderations, namely the crafty mike missions.
I did once suggest a slightly different idea, which could serve either as an alternative or as an additional feature to alternate starting corps. The idea I suggested was that we remove the standard progression mechanic of leveling up different corps, and instead have a singular level and experience bar. Then, every time the player levels up, they have the option to either upgrade a current license or unlock a new one.