I think the main feature haste is providing is Haskell to JavaScript compilation. That will increase your productivity by
1. Enabling you to lean on the compiler when refactoring.
2. Decreasing the time you spend debugging.
The fact that it will split your program into client and server side parts is scary though, and interesting. I'll have to investigate further.
(a) Does the abstraction actually lead to productivity gains in the long run, including time spent on debugging a possibly leaky abstraction?
It does if you're able to share libraries between client and server. Writing one module for a particular data structure and using it on both client and server is a huge boon.
(a) Does the abstraction actually lead to productivity gains in the long run, including time spent on debugging a possibly leaky abstraction?
(b) Does controlling these things manually enable you to provide a user experience that is sufficiently better to at least cover the costs of any lost productivity?
For any particular abstraction to be viable the answers need to be yes/no.
For abstracting away CPU/RAM communications the answers are clearly yes/no. But what are the answers for the abstraction that the OP referred to?