This already exists as a practical matter. According to current rules (specifically, the AC21 act), H-1B workers can start working at a new employer as soon an H-1B transfer application is filed by their new company. There is no need to even wait for the application to be approved. Applications to transfer H-1B visa are not subject to the cap, so there isn't that issue either.

H-1B employees are currently quite mobile. I have many friends who've switched jobs repeatedly during their H-1B period because it's so easy to transfer the visa. I honestly don't know where this whole "indentured servitude" idea comes from.

The part of the system that's fubared is the green card process, which can stretch for up to 10 years if you're from India or China. During a part of that time (not the entire duration), you can't switch jobs unless you want the green card process to be restarted, which affects mobility. But that is not related to the H-1B, and the solution to that is to fix the green card process.