Is there any advantage to cooking steak on the bone?
Well, many steak experts have held for years that bone-in steak just tastes better, something about that marrow being good.
J. Kenji Lopez-Alt from Serious Eats tested that theory.
He found that the steak bones were too impenetrable for the marrow to actually flavor grilling steak, but that the bones provided beneficial insulation:

To test this, I cooked four identical roasts. The first was cooked with the bone on. For the second, I removed the bone, but tied it back against the meat while cooking. For the third, I removed the bone, and tied it back to the meat with an intervening piece of impermeable heavy-duty aluminum foil. The fourth was cooked completely without the bone.
Tasted side-by-side, the first three were completely indistinguishable from each other. The fourth, on the other hand, was a little tougher in the region where the bone used to be.
What does this indicate? Well, first off, it means the flavor exchange theory is completely bunk—the completely intact piece of meat tasted exactly the same as the one with the intervening aluminum foil. But it also means that the bone does serve at least one important function: it insulates the meat, slowing its cooking, and providing less surface area to lose moisture.

He also mentions that the bone provides a framework to protect the shape of the meat, but it's a pain to carve the bone from the cooked meat:

The best way to cook your beef is to detach the bone and tie it back on. You get the same cooking quality of a completely intact roast with the added advantage that once it's cooked, carving is as simple as cutting the string, removing the bones, and slicing.

(The quote says &quot;roast&quot; but in the article he seems to be talking just as much about steak)
You mention that bone-in steak costs more at your butcher than boneless. I have not typically found that to be the case. When I have purchased steak, the bone-in has been less expensive than a boneless steak of the same weight of actual meat, cut, and grade of meat. I would sometimes pay extra for the butcher's time removing the bone.