Its entirely possible that Excelsior was imagined as a more routine/base level ship, but since the scene was cut in TWOK they just reused the name.
Pretty much this. The Excelsior in TWOK was just a random ship. They then reused the name for a completely different ship in TSFS. They also tributed the TWOK ship by showing an Excelsior in the Abrams films (a red, three-nacelled ship of the Kelvin family.)
That does pose an interesting question - if that line had stayed in TWOK, would Excelsior still be named NX-2000 Excelsior in TSFS? Compounded with the extra complexity of Sulu actually being given command of an upgraded NCC-2000 Excelsior by TUC.
Doubtful. They wouldn’t have wanted to confuse the audience by having the NX-2000 be the same ship as what they referenced in TWOK.