+1 - I'm not very good at playing altissimo, but I can reach all note I know how to reach on my 16 year old YAS-25. The only thing I'd add is that it's easier with some mouthpiece/reed combinations than with others, but that's borderline trivial (especially since I didn't find any combination that didn't work at all). The horn's perfectly capable of producing altissimo.Achieving the altissimo range is flexible enough by the sheer mechanics involved that it should NOT matter whether it is a student or pro horn and anything in between.
Granted, the interior proportions of some designs make some saxophones easier to achieve the altissimo range than others, but this can generally be compensated for by the throat, alternate fingerings, and MP selection.
You are likely not being held back by your horn in this area.