Why do colleges not send out more likely letters?

If they think that likely letters increase yield, why do colleges only send them to <20% of admitted students?

In general likely letters are only for the very top of the applicant pool.

Mainly because they work through applications in a procedural manner, meaning the mail would reach certain applicants past their decision. And once one gets behind a certain threshold, there may be clamor for colleges to simply release decisions as soon as they make them.

“In general likely letters are only for the very top of the applicant pool.”

Correct, but my question is why this is the case.

Are they really finishing 80% of apps past the point at which LLs would arrive on time?

The likely letter is an incentive to a top applicant. Its goal is to get a student excited about a forthcoming acceptance, so that the student will be more inclined to stick with the college that sent a likely letter.
They are sent to the very top students because all the others are a dime a dozen, to be frank, at least in their eyes.

^^^^Agreed. It is exactly that top 20% or so that the schools want to target and attract. The top schools will get plenty of people who want to attend so that isn’t the problem.

Because you are anxious to know if you got in ASAP but the schools work on a different timeline,

If colleges sent likely letters to 50% or more of the admitted students, the value of receiving a likely letter would be reduced. Part of the excitement of getting one is that you feel a sense of being wanted.

It really is a relatively small number, starts with kids they feel would be such a catch that they want to make that contact early, a special encouragement. Usually, those kids are heads above, in all the ways that college wants to build the class.