Why should their be rules on cherry picking? I see only a few provisions the NCAA could possible police; i) no student athletes shall be recognized or paid directly as if they are an employee and ii) general eligibility (including transfer rules)/academic enrollment rules, everything else is free market mania.
Pro sports can have tampering rules because its paid labor and for profit enterprise all operating under a collective contract.
The only reasonable curb to all this is to strictly limit student athletes to 1 free immediate eligibility transfer over their careers.
There is only one reason. If one can (still) believe that the education of the (student) athlete is priority one and that athletics is just an enhancement, then you can credibly argue that students hopping around to numerous schools is detrimental to that goal. The remedy to a free agent marketplace is to add a cost to transferring. Such a cost would be a disincentive to transferring for small bumps in NIL pay or minor disputes over playing time, coaching changes, or personal matters.
You can create that friction by counting transfer player scholarships as 1.5 that of a regular scholarship against the max or the number of years of eligibility remaining for the player, i.e., your transfer has 3 years left, that costs you three scholarships. They could be applied one per year or all at once. The idea of taking potential scholarships away from other recruits would not be popular. Another would be to make transfers sit a year and not granting a redshirt for it. You transfer, you only get to play 3 years in 5. Transfer after your freshman year, you only get two more. I'd still give graduates a free pass. I think that is a good incentive for everyone. Not 5th year players, ones that actually graduate.
Then we get to the real problem, tampering. It's a problem in the NFL and a real problem in the NBA. There is no reason for a school or its boosters to contact a player in another program. There should be severe penalties for doing so. There is no way to stop players who happen to know each other from passing messages, but undisclosed contacts should be punished. The NCAA has an interest in not having a free for all. The P5 power brokers have a different idea.