Some developers kind of already do that with Pre-order only betas and the whole "pre-order for early access to the beta" promotions.
I'm getting reminded of the days when magazines would give out demo disks, that was also a "paid demo" in a way.
It's a shame that demos have mostly gone the way of the dodo. I can hardly think of a publisher that makes demos these days, aside from Bethesda (DOOM 2016, Prey, The Evil Within 2, Dishonored 2 and Wolfenstein 2 all have demos on Steam), though they are all post-launch demos.