Does Stripe actually allow this type of use though? Does it have to be special agreement / account with them or just a regular plain stripe account?
They literally have a product for this use case, it's called Stripe Connect.
It's not a "hard problem" in the typical sense of the term. Money is not fundamentally hard -- the current state of financial law is what makes this hard. It's just a regulatory nightmare which makes this problem infeasible for random, unconnected people to try and solve.