Yeah, could just do the share issuance in 2 stages: the first at $0.000001 then later at >$1 to raise useful capital.

But multiple share classes often exist anyway for various reasons (different preferences upon liquidation, different voting polices, different retraction policies, different dividend policies, etc)

Yes

I believe Bain Capital used separate share classes to pump their employees 401ks

That level of collaboration and financial engineering should be encouraged