I think some of them do... probably not paying for all of it but I've heard of scholarships.
But a lot of that is probably after-the-fact. Reality is that if regionals just offered a bunch of money up front, there would be many takers, most of whom probably don't have the mix of initiative and ability to complete it successfully.
So an airline would have to do what the foriegn airlines do... heavy screening for ab-initio programs. There would need to be a difficult and detailed testing/screening process before they invest their money. In fact UAL is experimenting with this right now, look into that. If you're in the 1% of applicants they select you can skip the regionals and go right to a legacy.
For everybody else, the regionals want to see you demonstrate some ability before they start throwing money at you.