The altissimo notes do speak well once you learn how to "voice" them with your embouchure and all. And, I've found that they speak easier on a "register key on body" horn than they do with the linked register key.
Back in my high school days (almost fifty years ago - sigh), I was the nine day wonder, as I could jump about in the upper register on the bass with phenominal ease. My "audition piece" were the first and third movements of Mozart's bassoon concerto, and in the cadenza in the first movement, I was doing intervals, octave jumps and the like - it literally blew people away.
The trick of course was that I was a bass clarinet player (on an A bass clarinet no less, transposing the Bb music at sight) from the start, and had spent considerable time on soprano as well, and that I played an instrument that was "bash free". (The music director of the district literally bought a bass that was mine alone.) If you have the technique (all of those hours spent running scales and etudes written for the soprano clarinet as well as on the bass) and the working equipment, there's no limit to what you can achieve.
Of course, ask me questions about jazz chords and music theory, and I'd fail the test. That's what happens when your music instruction was limited to high school band and the school of hard knocks.
Last time that I tried it, I was still pretty good at transposing a Bb part on the A clarinet. Some old ingrained habits die hard.