When you reduce the cost of something by a large factor, it is often gamechanging. I think that being able to move a whole team
openly could reduce the cost to the new employer by a factor of three or more, which would be a significant change in the employment market, and change employer behavior.
Here is how I see it working out:
Lets say that Foosoft is a rapidly expanding unicorn, and Microgle is a cash cow which is going nowhere, and the employees are being squeezed by bad managers brought in by private equity. Foosoft is wants to expand rapidly to take advantage of their huge opportunity, so the are setting up entire new teams. Right now, they have to do so at a cost of X per employee, so ~6X per team, which includes the cost of recruiter fees, time of interviewers, team-setup time, and the initial inefficiency as the team learns to work together. X is going to be a substantial fraction of 1 year salary.
The cost is going to be pretty similar if a team migrates using the whisper route, as they won't all migrate across, the interview process is the same, there will be some new members, etc. X might be a bit smaller as you will have probably have fewer interviews as you found it easier to source candidates once your first hire made it in. But the your first hire might not have been from the team wanting to move.
Now instead suppose that the team from Microgle listed themselves on PoachMyTeam.com. Foosoft only has to check that the team is a good fit (it's a backend team, say, with capabilities they want). Then they interview the team lead and do group interviews of the team as a whole. Probably your interview process is 2X rather than 6X - you don't need to repeat everything for each candidate, because they already trust each other. Fundamentally, you don't need to check the capabilities of each employee individually, just the capabilities of the team. Also, X will be smaller because there will be less team setup, etc. So, a cost reduction of more than 3, at a guess. That degree of change is likely to change the employment market as a whole, at least in those areas where teams moving is likely to be practical.
But today, Microgle would sue PoachMyTeam.com for tortious interference. So PoachMyTeam.com cannot exist under current law. This is an economic friction caused by (private) regulation of the market.
As regards non-solicitation being mostly about clients, my most recent employment contract had a separate clause against employee solicitation as well as client solicitation.