Of the three semi-regulars, Zale, Rizzo and Igor, Igor (Jeff Maxwell) was my favorite. If they were going to make another regular character I would have preferred him.
Val Bisoglio appeared frequently on Quincy M.E which ran during the late 1970's// early 1980's the same as MASH. He may not have been willing to take on something that might conflict with his for sure gig even if it was just a few minutes of air time per week.
I think it would have been great to have Rizzo be the company first sergeant, giving direction to Klinger as the company clerk. The unit didn't have an enlisted leader and the chain of command didn't specify very much, except when Colonel Potter went away. I think the show would have benefitted from having an established chain of command to include Frank/Charles as the XO with their own level of authority. The enlisted leadership was completely lacking. Also, Margaret was the sole nurse with any authority and she really sucked at it.
Rizzo would have been interesting, he wasn't a part of the core clique like Klinger and would have challenged them a lot more and also been challenged as well.
I guess by that stage the producers weren't interested in developing/adding another core character and they also would have been worried about the loss of Burghoff. So Klinger was a safe choice.
Not to mention it was the Alan Alda show as well at that point.
Sometimes a movie or tv show plot is so stupid that only the stupid can understand it.