I wouldn't reduce them to that specifically, just that the underlying logic is that removing sources of problems causes solutions to emerge by default. The VIOLENT removal of problem sources is the extremist interpretation; more moderate thinkers just eliminate policies/laws/restrictions/freedoms that they think are problematic.
IOW, the belief that freedom (or at least efficiency) is what happens when you disallow the right things. If you want a better election, disallow certain voters. If you want a better military, disallow procurement restrictions... and then when you have a problem with procurement being wasteful and inefficient, it's time to remove some other restriction or remove some osbtacle to competition that must have caused that problem... we'll just keep banning things until we find the thing that caused the problem!
But to backtrack: the EXTREMIST interpretation of that philosophy assumes that if the best way to empower "the good guys" is to kill all the bad guys. If the good guys aren't in charge, it's because the bad guys are still an obstacle and you haven't killed enough of them yet. You just keep hacking your way through roomfuls of politicians until one of the good guys happens to fall into power. Of course, the definition of "good guy" is "Somebody who doesn't make trouble" which is not always or even usually the same thing as being a competent leader. This is the troubling implication of "Inter Arma" in DS9, IMO. They installed a Pro-Federation politician in Romulus in favor of a nationalist, purely because they knew the nationalist would always do what was best for Romulus even if it meant turning his back on the Federation. This is troubling because they're recognizing that allying with the Federation MIGHT NOT be the best thing for Romulus, but the guy they installed into power is not capable of recognizing that. Admiral Ross and 31 didn't want a competent leader, they wanted a leader who wouldn't cause problems for them.
But as I said, it's possible Section 31 isn't going to play it entirely straight this time. Xenophobia and ultra-conservative racist nationalism have become mainstream again to a degree America hasn't seen since the the 1960s. If the writers want to make a comment on how persecution of Otherness can go very wrong very fast, Section 31 is the appropriate vehicle to do this, especially given their apparent absence in the 23rd century as we otherwise know it.
And how do you think they GOT this way? It wasn't by soul searching and logical analysis, and it probably didn't happen all at once. It definitely didn't happen to everyone everywhere in the Federation either, otherwise people like Mudd or Lorca or the other two assholes on Burnham's prison shuttle couldn't exist.
The struggle to produce a more constructive social contract is just that: a STRUGGLE. It evolves in stages, you fix one thing and then you fix another, and then you find out the thing you fixed doesn't work the way you thought it would and you fix it again. Sometimes you backslide; the thing that got fixed and is working just fine is now being challenged and you have to justify it all over again (70 years later, we're still trying to keep them from cutting social security? REALLY?) These are not problems you can fix just once and be done with them. You have to fix them over and over and over again and keep fixing them to make sure the problems get solved every time they come up.
And another important thing to remember: you cannot actually eliminate problems just by eliminating the source of them. A new source is ALWAYS available. Even if you kill every last person in Section 31, there are enough people who think like them that they'll eventually just start it up all over again and you're back to square one. This may not even be the same Section 31 Malcolm Reed worked for a century earlier; for all we know that outfit got blasted into atoms by the Romulans and somebody started it up again in homage to them (like the "Sons of Liberty" or something). And here too is a lesson for us: eliminating Section 31 and all the people who agree with it won't make it go away. Driving it underground won't make it go away. Hunting them down ruthlessly and turning them into exiles certainly won't make them go away.
So what would be the constructive solution to Section 31?
What would be the Starfleet solution?
