Why do military departments debate operational training budget drawdowns and still employ hundreds of thousands of civilian employees?

PO3 Aaron Hassay, LTC Jason Mackay hit the nail on the head.
First civilians generally cost less across the board. When they cost more, their specialty is not readily available in DoD billets. LtCol Robert Quinter also highlighted that employing uniformed personnel affects staffing levels in operational units. So budget wise, in a slimmer uniformed services count, it is cheaper and more efficient to hire civilians for certain billets.
Second, operational training budgets are a different animal than personnel overhead budgets. I know ultimately it is all the same money if you go up high enough, but whomever gave you the excuse that you couldn't go to school because there was no money was either making stuff up or is horrible t their job.
In the Army, we forecast training quotas a year in advance (earlier if you have a steady state) and request budget allotments to go with the seats. I am confident the Navy has a similar fiscal process as leaving training budget allocations up to chance is not something the military typically does.
A civilian's pay is already calculated in the budget so it is a sunk cost to the budget folks.

CSM William Everroad - PO3 Aaron Hassay to amplify, what happened before you or I ever got to the military, there was a wholesale reduction in the operational force after desert storm aka the Peace Dividend. Probably around the time we were born, the civilian workforce were resourced to fill the institutional and strategic levels of the Department. As the CSM states, it's sunk cost. When the draft ended and post war troop caps come by federal law, this allows the services to maximize troops on the line where they must be uniformed personnel instead of shaving off people to run the installation, institutional and strategic levels of the services. Those personnel dollars, even at the congressional level are not the same allocation (referred to as money coloring, i.e. Not the right color of money) of funding as Training dollars. Even if they fired 100 civilians, paid their unemployment benefits (losing employer pays, yep...the Army alone pays 11B dollars a year for ETS soldiers and civilians), assume we see those dollars the following year, we could not use it to pay for a bunch of TDY and class seats as it isn't colored for that. Any military or civilian spending it for that would be breaking federal law under the Anti Deficiency Act. A law passed to prevent primarily DOD from spending federal money outside the appropriation process or obligating the government without authority to do so (without a contract Warrant or an appropriation to cover the contract).

Money is appropriated as annual, two year money and five year money for MILCON. It can only be spent on that appropriated purpose which is pretty specific. If there is money left, it has to be be reappropriated through the congressional budget office. In which case they might just take it all back or ignore the service request and maintain the appropriation or allocate it to another different allocation. Expiring appropriation dollars that can't be obligated (actually spent on a good or service with the dollars going to the vendor) by 30 Sept go back to the treasury on 1 October and are used to service the national debt principal. From a ship or an O6 level command, were talking budget dust, may be 10s of dollars. I spent everything but 12 cents out of $60M my last year as a Garrison Commander. That gets swept up by the higher command levels and may wash up as a million or more, but that is every program, activity, and color of money put together and is deceptive as to its spendability. I tried to reprogram money to contract for something I was directed to do by law, regulation and Army EXORD and I was not only told no, but was chastised because that color of money was only spendable and authorized to be obligated by the Army CIO G6 under a specific program of record.

I've heard of SWO in a box, agree that is an abysmal way to come at a training challenge. I've also never agreed with the unrated enlisted thing in the Navy. It reflects more than dollars, its service culture: the thinking was that the only place you really learn anything of value is on the deck plates of a ship. It's why until recently (2007ish) Naval Officers either attended the Naval War College as an O4 in the CNCS or an O6 at the war college level but rarely both. I understand that most of the SWO qualification is onboard and underway using a certification packet under the supervision of the Exec. The two weeks at Newport TDY was explained to me by SWOs as a rounding event to balance out SWO experience between hull types. The unrated enlisted has been a decades on decades tradition of the Navy that transcends budget woes we grew up with since the end of the eighties. Apparently no CNO, major CMC, or combatant commander has raised it as an issue, so business as usual.