One problem with your argument: that is done by fascist regimes. For the Nazis it was The Law for the Restoration of the Professional Professionals which fired thousands for the obvious reasons and also if you weren't an actual Nazi. Pinochet fired thousands to cut government spending and as an excuse to get rid of non-supporters from the ranks. Also, it was to get rid of state-sponsored industry in many sectors to have them more privatized since in many fascist states it is the private industry that benefits from fascists with de-regulation of their businesses, collecting government contracts without many strings attached. Regulations DO show up...but not in the way you think: they are used as punishment to non-supporters and as ways to consolidate power.
You used education as an example. What we see in fascist societies when it comes to education, it gets privatized...with the understanding that they follow The Law for the Restoration of the Professional Professionals. So, it's not really regulation so much as consolidation of power. Here's what an educator experienced in 1933 (Peter Drucker):
"Frankfurt was the first university the Nazis tackled, precisely because it was the most self-confidently liberal of major German universities, with a faculty that prided itself on its allegiance to scholarship, freedom of conscience, and democracy. The Nazis knew that control of Frankfurt University would mean control of German academia. And so did everyone at the university.
Above all, Frankfurt had a science faculty distinguished both by its scholarship and by its liberal convictions; and outstanding among the Frankfurt scientists was a biochemist-physiologist of Nobel-Prize caliber and impeccable liberal credentials. When the appointment of a Nazi commissar was announced . . . and every teacher and graduate assistant at the university was summoned to a faculty meeting to hear this new master, everybody knew that a trial of strength was at hand. I had never before attended a faculty meeting, but I did attend this one.
The new Nazi commissar wasted no time on the amenities. He immediately announced that Jews would be forbidden to enter university premises and would be dismissed without salary on March 15; this was something that no one had thought possible despite the Nazis’ loud antisemitism. Then he launched into a tirade of abuse, filth, and four-letter words such as had been heard rarely even in the barracks and never before in academia. . . . [He] pointed his finger at one department chairman after another and said, “You either do what I tell you or we’ll put you into a concentration camp.” There was silence when he finished; everybody waited for the distinguished biochemist-physiologist. The great liberal got up, cleared his throat, and said, “Very interesting, Mr. Commissar, and in some respects very illuminating: but one point I didn’t get too clearly. Will there be more money for research in physiology?"
The meeting broke up shortly thereafter with the commissar assuring the scholars that indeed there would be plenty of money for “racially pure science.” A few of the professors had the courage to walk out with their Jewish colleagues, but most kept a safe distance from these who only a few hours earlier had been their close friends. I went out sick unto death—and I knew that I was going to leave Germany within forty-eight hours."
That's punishing those who don't toe the party line. That is not regulation. Because the university mentioned here was funded by wealthy Germans privately, even though its admission policy was one of public use. After WW2, it would become a public university, but at the time of Hitler's ascension, it was not.
Now, there are exceptions to the rule, I will grant you that, but they are exceptions. However, you see mass firings of government in both fascist and authoritarian regimes. Pol Pot, Stalin, Tojo, etc. It's all about consolidation of power. Trump, I will grant you, dances on the edge of but hasn't committed just yet.
The reason why folks view Trump as a fascist is because he is not genuine in his desire to cut spending: we are actually seeing this now. DOGE was a consolidation of power, getting rid of those who might be a problem. Honestly,. DOGE was a purge done very poorly. Trump is attacking education that won't support him...again poorly. Department heads who are not really qualified to lead said agencies, usually have skin in making profit on the area that agency may affect. We are seeing regulations that punish, but do not reform...these are the reasons why (among many more) that folks think Trump a fascist.
The reason why he technically not really in that ideology firmly is simply due to his incompetence: he makes a better authoritarian because he would suck as fascist. But there have been "leaders" who turned out to suck as fascists, so you can't rule Trump out of becoming one.