The irony there being that the original USS Excelsior herself is in the Starfleet Museum and clearly wasn't kept in service forever. Behind-the-scenes information from PIC S2 suggests that the Excelsior was retired in 2320 after 35 years of service, though this was possibly a political decision since it coincided with Sulu's own retirement from Starfleet.
It does seem odd that we know so little about the fates of some of the starships Enterprise. I get the argument that "it leaves the possibility open for future stories" – but then the only Enterprise ever properly revisited is the original 1701 in DIS and SNW, and its history is already extremely comprehensive.
Its also possible that the Excelsior, being a prototype pressed into regular service, had some unique construction and equipment fits that made it impractical to continue long term.