Just the opposite I think. I can only think of a handful of flagship universities in the state's (current) capital city. I think a lot of 4-year universities went with more of a "pastoral" approach (ie, rural). Or else, as has been suggested, capital cities/major cities had not yet been settled at the time the university was founded.

flagships in capital city that i can think of:
LSU
OSU
South Carolina
NCState (do they count as "flagship"?)
UTexas
UWashington (well close)
Wisconsin
Minnesota

Just a few of the many outside:
UGA, Bama/Auburn, UTenn, UF/FSU, Ark, UK, Ole Piss/MSU, Michigan, Purdue/IU, Illinois, PennState, Maryland, UVA, WVU, UMass, Iowa, Nebraska, Kansas, Okla, Colo, Arizona, Cal, Oregon

sure i skipped a bunch but you get the idea

It was Pineville to be exact which is very close to Alec. I beleive that most of the campus burned and it was moved to downtown Baton Rouge and then to it's current location in the 1920's.

All ii know is that Ole Piss is in Oxford. When LSU is playing there it becomes our property and we will own it.

When we have taken our fill with winning bellies we will turn it back to the sheep and goat lovers.

Geaux Tigers