That the character of Hot Lips could loosen up and be part of the gang was more
plausible than that Frank would. He was portrayed as on the brink of a breakdown
from the start. When Frank and Hot Lips were transferred to the series both
characters were toned way down. They both were portrayed as just overzealous as
a counterpoint to Hawkeye and Trapper John.

Burns sticks around in this movie for about the same amount of time he sticks around in the book. It had nothing to do with Duvall and Altman.

I heard Robert Duvall had problems with Altman & that might've been a factor in Burns' early departure. We all know Gould & Sutherland also had issues with their director, but there would've been no way of ditching either of them, even if Altman had wanted to.
But since they hardly followed the script, I think Altman could've kept Frank Burns around longer, had he wanted, like he did with Kellerman.
Marriage is between one man and one woman, to the exclusion of all others.

But a memorable one. That straightjacket was a good fit.

Yes, read the book. It will make more sense.