Why? The first answer is that Mozart composed it for basset clarinet (not the basset horn, which is a different clarinet, and even lower pitched); and from this the second reason follows: Mozart wrote for the full lower range of the instrument in some of the key passages... Including my very favourite passage - the one that is, for me, the climax of the whole (exceptionally well-integrated across-movements) concerto.
This passage is in the 'middle' section of the last movement, it is the descending 'sequence' in which the same pattern of intervals is repeated going down the scale.
Hear it first, as written, on the original basset horn - tuning in from 23:45 with the sequence starting at about 24 minutes...
But if this is performed (as has been usual practice) on a standard B-flat instrument, then it runs out of low notes after the statement of the sequence - so the player has to go up an octave for the second and third cycles of the sequence.
This performance has similar timings - you should start at about 23:55 and the sequence begins at about 24:10.
Of course, this is just a few seconds in isolation - and you should really listen to the whole movement to get the musical shape of it. But I think you will agree that (setting aside the quality of performance - neither of these being top-notch) the musical sense is far superior when the notes-as-written are performed - and there are other instances here and there though the concerto.
In conclusion, Mozart's basset clarinet concerto K. 622 is (ceteris paribus) best done on... a basset clarinet.