Well, the problem with YouTube is ever since like 2010 or so, Bagdasarian has really cracked down on people posting Chipmunk content of any kind, so it's really difficult, unless you were to try another site like Dailymotion or vimeo.
But Drtooth has said it many times before, there really isn't a whole lot of excuses for THE ALVIN SHOW to NOT be on DVD, but I guess maybe there really isn't a whole lot of market for it? I don't know, but really, yes, by all means really, there's no reason why a complete series set of THE ALVIN SHOW shouldn't happen.