Bill Snibson said: "Tour casting is just such a different beast. Broadway names really don't do anything for box office across the country and only cost production a larger salary. Looking at all the current tours out right now, the biggest "names" are Richard Thomas in TKAM, Norm Lewis in Soldiers Play, and Adam Pascal in Pretty Woman just for some comparison."
That's the thing, and I agree with Valentina's point that even they're not names that will sell tickets. Over the years, I can't think of too many names that sell tickets in any touring productions I've seen - and I live in a fairly large market, San Francisco, that sometimes gets actors who want to be on a West Coast swing that includes Los Angeles.
The only examples of star casting I can think of are mostly minor: Betty Buckley in Hello, Dolly!, Darren Criss and Lena Hall in her Tony-winning role in Hedwig and the Angry Inch (she also played Hedwig a few times), Carmen Cusack recreating her starring role in Bright Star. We'll occasionally get Broadway stars, as when Joshua Henry played Aaron Burr during the first Hamilton tour, but the show was the star. We got really good seats to Bright Star because, as good as Cusack is, she's not a star. I don't think Buckley was that much of a draw as Dolly, although she did a fine job. They're trying to promote Into the Woods as a "straight from Broadway" star vehicle, and that may have worked to some degree (they're charging premium Broadway prices for good seats, at least in San Francisco), but it's more the musical itself that's the draw.
As for Company, I'm not expecting big names but I am interested in the casting - because I plan to see it next year and would like it to be good. But I suspect I won't have seen most of the actors in anything before.