A reasonable definition of "primary qualification" is that feature which most significantly narrows the set of candidates under consideration.
There are hundreds of thousands (millions?) of people with a similar or greater military record.
There are probably less than a dozen who have a clearer record of being a yes-man (by virtue of very few people being on TV to begin with, and even fewer willing to rhetorically fellate POTUS unconditionally)
You intersect the two and you get Hegseth, but the criterion that did the heavy lifting is absolutely the yes-man one.
Trump saw him and liked him on TV
Trump made him SecDef