I think if you look at any Buzby Berkeley musical, you can see how the casts could number over a hundred, sometimes two! So, to have an actor who did all three, and well, was a hot commodity.
Nowadays, to succeed on the boards of Broadway, and get roles in the musicals, you need to be able to do all three very well. There are plenty of people after those limited jobs, and if you can't do it all, there's someone right behind you that can.
Meanwhile, if you're a big name actor with major marquee value, this can be forgiven. So, when this actor was announced as taking the lead in a revival in a Broadway musical, I figured he'd either dance or sing well. Dancing can be taught to the point that someone can pass muster for eight performances a week (or one movie, like for Natalie Portman).
A friend posted this link yesterday and I was transfixed, because he truly is a Triple Threat:
Now I've got another Broadway show I'd love to see!