The H1 visa prohibits all paid work except for the sponsoring employer. This lock-in is precisely what makes these visas lucrative to TCS etc. Removing the lack of mobility will remove a big perverse incentive.
Which makes me doubt whether this step would make any difference to the problem of H1B abuse. However, it would make a HUGE difference for those who are not abusing the system.
Disclosure: I'm on an H1B visa. Of course I want it to be easier to change employer. Who doesn't? Its like a fundamental right.