If an LAC has adequate resources, I do not see any reason why an LAC cannot enroll 10,000 or more students if there is sufficient demand.
To the best of my knowledge, the largest schools categorized as LACs enroll about 3,500 undergraduates (Bucknell University) but tend to offer non-LAC pre-professional programs such as engineering & business.
Whether or not LACs can grow depends in large part upon consumer demand. I googled:
“Are liberal arts colleges changing their mission ?”
“Can liberal arts colleges survive ?”
Dozens of articles appear. The article below shares that a survey revealed that 40% of liberal arts graduates would change their major if they could. This, of course,suggests that LACs might be shrinking rather than expanding.
I recently read a news release that St. Lawrence University in upstate New York is adding majors such as finance, data analytics, and business in the liberal arts. Interesting twist is that students who major in either finance or data analytics must also choose a second major in the liberal arts.
Based on the articles that I saw, it appears that the best ways for LACs to expand is either through mergers or by offering non-liberal arts courses of study such as business & engineering.
While the most elite LACs can remain highly selective due to the number of applications received each year,most LACs are in need of more students in order to sustain the school.
If the change in MBA programs is any indication of future demand at the college level, then technology will be the primary growth area in higher education at the expense of less technical course offerings.
Competition from China may also be a factor that raises demands for pre-professional undergraduate courses of study, but that is a topic deserving of its own thread.
STEM seems to be the fastest growing area of higher education.
P.S. The simple answer to OP’s question: “If it is at least theoretically possible for an LAC to be that large, what would be the reason why LACs are generally small in practice ?”
Simple answer: = Lack of demand by consumers & by employers.