I just can't think of many college programs where (i) a coach could have both the mandate to give "never punt" a sustained try and (ii) it would have chance of working.

Bad punting decisions can haunt a coach for the rest of their career, and quickly become a rallying cry for a change of management (consider "4th and 19"...)

Big teams can win anyway, even with punting. They may go for it on 4th and short, when the analytics favor it, but why jeopardize the good thing they already have going?

Bad teams won't be able to consistently move the ball, even if they do convert the odd 4th down here or there (does anyone who watched BYU vs LSU or Michigan think that BYU would have lost by less if they had gone for it on 4th?).

This leaves a bunch of middling teams as the most likely to try a "never punt" strategy—but those middle of the pack programs have expectations that often surpass their level of prestige, and won't put up with a strategy that costs them some wins in the short term.

And of course, all of this ignores the fact that many teams have defenses that are better than their offensive units. Never punt, and you keep your best unit off the field.