Yes, this is what Ur/Web does albeit this is limited to Web Server requests. I'd argue all programs could be short lived and memory management becomes a matter of sizing program's scope/role to the amount of memory you can greedily consume. Certainly many sorting program (for e.g.) can leak until they terminate. Then, cheap instantiation and communication between programs.
That's no different than writing a traditional program and using big arena allocators for everything instead of individual allocations, except it's more complicated for no apparent reason.