I've had a few more thoughts on the budget issue.
Not only is 2.4 million basically a rounding error compared with the budget we're talking about, but we would almost certainly not save 2.4 million by expelling trans people from service.
Unless I'm misinformed, the military is not overstaffed, so discharged soldiers would either need to be replaced, or the effectiveness would suffer.
It's hard to exactly measure the cost of replacement. I believe it currently costs something like $6.5k per recruit. That comes from about a billion a year in advertising, staffing recruitment offices, enlistment bonuses etc.
We don't know how many trans people are currently serving, but even conservative estimates make something like at least 3,000 pretty likely.
So just in recruitment costs, for just the one time replacement we're looking at $19.5 million.
Now we'd also be throwing out all the training that these people received and having to spend on training all new people. Some of these trans people seem to be quite advanced in their training, but to be generous and simple, let's just look at basic training. There are a variety of numbers, but it looks like at least 50k to bring one soldier to readiness.
So replacing 3k trained soldiers would cost about $150 million in replacement training.
There are a million other smaller costs, like simply filing paperwork (not a small thing in a bureaucracy the size of the US military) updating recruitment paperwork and every system that has to list requirements. Fighting the inevitable law suits. Shipping people home from overseas posts and shipping in their replacements. And on and on. It's very likely that the minutiae would end up costing more than the direct $169.5 million of the one time replacement.
But even leaving that out, it would take 70 years of saving 2.4 million a year for this to break even. Now charitably again, I can imagine that all things being equal, more trans people might serve in the future, and the costs of medical procedures might rise, so let's say 50 years.
(Realistically, all the real costs likely mean it would be more like a century before this policy broke even)
This is of course leaving out continuing costs. If we've got a ban, then every so often they're going to have to discover trans people and kick them out. If we're leaving out a segment of the population, however small, we're going to have to spend more yearly on recruitment. You're probably going to turn off some potential recruits who view this action as bigoted.
If this were actually a budget saving measure, it would have originated with a study of all the economic factors above and more, instead of a tweet.