Your logic makes sense, but I think the seating capacity might be a deal breaker Brown. Tidewater's 7,500 capacity should be OK for most games, but it isn't enough for the Brown Bears' signature event - the Harvard game - which regularly draws in the realm of 10,000 fans (or more). I have a hard time imagining the University hamstringing themselves like that just to play somewhere a bit nicer. And while the current stadium is certainly an uncomfortable relic, it is historic and I can see that carrying a lot of weight for a storied Ivy League institution like Brown who might view moving to a new modern facility as "selling their soul." That's why I thought PC would have made sense (prior to Anderson, anyway) given their relatively recent rise to prominence in soccer and their existing willingness to play off campus in a larger, modern(ish), non-school owned facility.
Admittedly, I know nothing about lacrosse. So if PC or Brown (or someone else) has a program that's good enough to warrant playing in a larger stadium, maybe that'd work. But if not, I just don't see any local college taking advantage of the new space.