If you sign a contract with an agreed penulty for misrepresentation you can be liable for that—which is nothing akin to your birthday cake example.
And there are all kinds of ways a college can claim harm for signing, say, a team athlete who can’t play the sport or just any student who brings down the quality of the student body or doesn’t diversify it in some way they are seeking. A whole lot of damage from that? Probably not.
But don’t the charges in these college cases include commercial bribery that via wire communications or otherwise crossing state lines falls under federal purview? https://en.wikipedia.org/wiki/Commercial_bribery
In the case of a college application, the penalty is what? The college cannot unilaterally declare that a misrepresentation is a criminal act ... so this would have to be a civil matter, not a criminal one. But keep in mind that the applicant pays a fee to the college, so there is no "duty of care" relationship that would apply like you would see in a customer-business transaction. If anything, the college has a duty to the applicants that is not clearly reciprocated by the applicants (as I read it).
And there are all kinds of ways a college can claim harm for signing, say, a team athlete who can’t play the sport or just any student who brings down the quality of the student body or doesn’t diversify it in some way they are seeking.
You can throw "diversity" out the window because it's impossible to quantify it, or (more importantly) to quantify the financial benefits of it. And the case of a student who misrepresented his or her athletic skills would never hold up in a court of law, since this would be a classic example of a plaintiff failing to take steps to protect its own interests by scouting the student before signing a commitment letter.
The commercial bribery angle might be more applicable than any other, but the link you posted seems to undermine it: "There is no federal statute that by its terms expressly prohibits commercial bribery generally."