what tier of liberal arts colleges are you talking about here? the president at the college I attended made over $400k base and that was five years ago.
https://www.bostonmagazine.com/education/2017/12/11/boston-u...
"Robert Brown earned nearly $2.5 million in 2015, according to the most recent tax filings." (President of BU)
"Three other leaders had seven-digit earnings in 2015: Harvard President Drew Faust, who will retire at the end of the school year, earned $1.57 million; Northeastern President Joseph Aoun notched $1.45 million; and MIT President L. Rafael Reif took home $1.03 million."
Maybe the OP isn't talking about the same tier of school, or maybe Boston is an unusual place for university president salaries, but those numbers are pretty far from $200k.
I'm talking about places with words like "south eastern" and "central" and "state" in their names. And SLACs with endowments below ~100M. In other words, I'm talking about the vast majority of universities and colleges -- the ones that aren't (literally) Harvard or MIT. Places that don't have phds programs, and maybe don't even have sizable masters populations.
Conditional on them existing students are forced to attend in order to keep up in the credentialism race, but a supra-market force like the federal government could impose a more globally efficient solution.
(Even at 400K, "highly paid administrators" doesn't pass the smell test.)