There would have been a sense at the time that a "civilian" pilot would be less provocative and more deniable, and would enjoy slightly more credibility while claiming he was on a "weather mission" or "had navigation problems".

The names of all US military officers are a matter of public record (and the soviets had the entire list), so that would only add fuel to the fire.

It's also possible that the USAF didn't WANT to be doing that...they were always conscious of public perception and may have preferred not to risk a high-profile failure w/ international media circus. Assuming they were even given a choice in the matter.