Rings can heal and teleport, though the second use we haven't seen since Crisis and the first only seems available to people who don't know any better (Ice did it with Guy's ring, and Guy has never been able to duplicate it because he "knows" it isn't possible... much the way the yellow weakness has been retconned). I don't think there's any reason to think a ring couldn't make a Boom Tube whatsoever. On the other hand, there's fair reason to think there aren't many Lanterns who could make a Boom Tube. Motherboxes are fundamentally user-friendly, while GL rings are manifestly not.
Actually, there's the solution - there are various New God Lanterns in the various mythoi. Do they still carry motherboxes, and if so, why did they bother to accept rings in the first place? If your society has access to guns, a crossbow-wielding military service isn't going to hold much appeal for you as a way to make a difference in the world. I think we're looking at something more like a laptop/hybrid car distinction - two devices only comparable in the most broad terms, given the disparity in purpose and the cultural take on usage between them.