Decades ago, I think that's the sort of thing Comedy Central started with---they showed some 1950s TV comedies (including Steve Allen and Ernie Kovacs) and, IIRC, some vintage comedy films. But they "grew out" of that into producing their own programming.
It's a Catch-22---no one runs a channel like that because not so many people know those comedians anymore---and no one can discover them if they aren't shown for new audiences. Name recognition = marketability, and if a name drops off the pop culture radar, they're pretty much gone forever. I cringe whenever I hear "Laurel & Hardy? Who are they?" But that's the way it is today.
That's such a shame.... I miss the older tv shows and movies. You know, half the time, I get to looking thru the guide on the TV, and I say to myself, crap, crap, seen that 10 times, nope, no interest there, crap, crap and more crap. I turn the TV off and turn the laptop on.