It is no coincidence that Linville's replacement (Winchester) had the same prime character traits as Burns (noted above). Above all else, the antagonistic, stuffy man disrespecting the jocular habits of his fellow surgeons.
The producers of M*A*S*H
had a tendency to replace characters, when necessary, with new characters that would occupy the same function but in many cases were opposites in personality to the character being replaced. Making a vague generalization like "stuffy" about Burns and Winchester just papers over their extreme differences.
The function both served was as an antagonist and foil for Hawkeye and B.J.
Frank Burns was reflexively conservative and insecure, a mid-westerner who sought after professional and military status but was regarded as a mediocre surgeon at best. He was a whiner. He invariably came out on the short end of jokes.
Winchester, OTOH, was a Bostonian, born to status and wealth, very well educated and anything but insecure - he knew exactly how good he was and was aware of the virtues as well as the limitations of the other characters. He was a highly skilled, expert heart surgeon who could instruct doctors in the unit, and finally he not infrequently turned the tables on his tent mates' attempted practical jokes.
Burns was always a step behind the others, Winchester often a half-step ahead.
There are similar sharp contrasts between Blake and Potter, and Trapper and B.J., and all were by design.
OTOH, there's nothing that Kirk says or does in WNMHGB that would have been "out of character" for Pike because so little character was established for either of them at that point. Roddenberry simply replaced one handsome leading man of a certain apparent age with another.