^ For the same reason that shows like million dollar quartet and even Ring of Fire toured. MDQ ran for a while but at really small houses, and ring of fire ran for a hot second. MDQ is still touring - somewhat successfully - and ring of fire chose markets to play in that would appreciate the Johnny Cash brand.
A lot of times producers just want the brand name of broadway stuck on to their tour. If you advertise with "direct from broadway!!" it can be a great marketing tool. Also, when the rights are eventually sold to regional and community theatres, it's a big deal. If/when the show wins a tony for score or any other award, that's a HUGE selling point right there.
Bridges, if it happens (and the producers want it to happen), will most likely route the show into cities that would appreciate the source material (Midwest?) or take a route similar to that of Light in the Piazza.
-There's the muddle in the middle. There's the puddle where the poodle did the piddle."