Carol Burnett was asked that question at a seminar I attended a few years ago.
"Way too expensive," was her answer. Mind you, she was talking about REAL variety shows, not glorified amateur hours like American Idol or even the kind of shows Lawrence Welk and Mitch Miller used to do--which were just bands and singers playing and singing.
No, she was talking about real variety shows, like Dean Martin, Smothers Bros., Garry Moore, Flip Wilson, Andy Williams, Ed Sullivan (sort of), Red Buttons, Sid and Imogene (Your Show of Shows), Uncle Miltie, and of course, Carol Burnett.
With honest-to-goodness variety shows you spend a fortune on sets, costumes, writing, music clearances, orchestrations, orchestras (or at least pretty decent-sized bands) and top-name talent week after week. Big money, which the networks are not willing to spend when they can run amateur singers, dancers, whatever, out on the same stage night after night and let them do their best--for pennies on the dollar.
Plus, Carol would never say this, but I will: assuming you wanted to do a variety show, where will you find people with the grace of a Garry Moore, the world-class comic genius of a Carol Burnett, the unblelievable writers from Your Show of Shows (Mel Brooks, Carl Reiner, Selma Diamond, Neil Simon, and others of that ilk all in the same bloody room writing a TV show!). No, we shall not pass that way again. TV was young and brave then, and it had visionary leaders like my old friend and colleague Frank Stanton, who honestly believed that the phrase "Thank you for allowing us to come into your homes" really meant something. That was an expression of the serious responsibility that early broadcasters felt for their audiences.
Just the ravings of an old fool, I suppose. But maybe not. After all, we still have those old tapes and kinescopes to help make the point. I'll watch those.
In any case, you're not going to see any new variety shows of the kind we remember so fondly. Not gonna happen.