I agree that the high ranking military are compromised and tend to be DS political stooges in uniform, but don't forget the ratio...

There are thousands of rank and file soldiers to every high-level officer. The soldier vote would greatly outnumber any of those in high levels of leadership. The average soldier by and large is super red-pilled due to being exposed to how the world truly works. Very few people leave the military as registered democrats.

So long as a soldier's vote is equal in weigh to a high-level officer's vote (as it should be) then I do think that Heinlein's idea would still work.