It wouldn't be unprecedented to do something like that. The L didn't start out up front where it is today. Originally, we talked about GL and GLB. You can still see that in the legacy names of organizations that were founded a long time ago, like GLAAD and GLAD. (GLAAD is a national queer media advocacy group. GLAD is a Massachusetts civil rights group.)
Moving the T up front isn't a bad idea, in my opinion, though off the top of my head it seems to me that there would be an order of magnitude more work to do today than when we moved the L up front. There would be just so many more changes to make, practically speaking. And given resistance to change, there would probably be a lot of pushback. Maybe more than it's worth? I don't know.
But it's certainly worth thinking about!