For just bagging the peaks, your plan would work, but in my opinion, it misses the best of that region. The South Rim is a much better hike than Emory Peak. Emory gets you about halfway there before you peel off and summit, but it’s not the best half. If you go back down after submitting, you missed the entire south and east rim, which I think is the highlight of the whole park.
I also like the desolation of getting a campsite somewhere in a very remote spot, and just chilling out for a day without seeing a single other personal vehicle, but I understand that’s not the vacation you’re looking for.
Almost every trip I’ve taken to Big Bend Ive roamed around a bit and rarely camped in the same place more than once or twice. I always head home feeling like I was on the move a little bit more than I wished I had been and wishing I had just focused on a single part of the park for longer periods of time.