Could Beethoven have composed a Cello Concerto? Wouldn't it have been great? I guess. Maybe. Not everything that Beethoven composed was wonderful. Did he even want to compose a Cello Concerto? He certainly could have composed a Cello Concerto if he wanted to do it. As it says in the OP, Beethoven composed five Sonatas for Cello and Piano, but he also did the fun and vibrant Triple Concerto for piano, violin, and cello; which I'd take any day over the mystery Beethoven Cello Concerto that may be hiding behind "Curtain #1". Likewise I'd certainly keep the even better, and more masterful, Brahms Double Concerto and the two achingly beautiful Brahms Sonatas for Cello and Piano, over the imaginary Brahms Cello Concerto that lurks behind "Curtain #2".
Maybe it is fate or destiny that the world's greatest cello concertos would belong to a less popular composer such as Dvorak, and not to a superstar like Bach, Mozart, Beethoven, Brahms, or Tchaikovsky.
And since the high and the mighty couldn't find the time or inspiration to compose that mystery cello concerto that we might wonder about, isn't it great that Dvorak made up for it with his own monumental Cello Concerto, arguably the finest in the genre? And now that I think of it, almost all the great cello concertos belong to composers outside the realm of the ones who think of as the "superstars"; not to Bach, Mozart, Beethoven, Brahms, or Tchaikovsky; but to Dvorak, Elgar, Shoatakovich, Barber, and Britten (if you count the beautiful Cello Symphony that Britten wrote for Rostropovich as a cello concerto). But Wait! There's also Kabalevsky, Myaskovsky, Hovhaness, and John Williams of Star Wars fame, whose Cello Concerto that he composed for Yo-Yo Ma, is very solid and well-crafted, even if not exactly a masterpiece. And would you really want to trade it all, for the mystery Cello Concerto by Tchaikovsky that may be waiting behind "Curtain #3"?
As for a Brahms' Clarinet Concerto, I'd say that Mozart pretty much ruined it for almost everyone with his utterly serene and lovely Clarinet Concerto; far and away the ideal. Carl Maria von Weber left us with two Clarinet Concertos that I find to be mildly entertaining. Carl Nielsen also composed an ambitious and interesting enough Clarinet Concerto that is to be admired at least for the effort. Then the likes of Stravinsky (with Ebony Concerto); Aaron Copland (with Clarinet Concerto); Leonard Bernstein (with Prelude, Fugue and Riffs); and Morton Gould (with Derivations for Clarinet and Jazz Band); composed some wildly fun and entertaining jazz-inspired music for clarinet and orchestra (Copland's is the most masterful); but that's about it.