Is it actually a deterrent in the USA though? Do you see signs of a heavily armed populace actually deterring lethal shootings and paramilitary action by the police in the US?
If anything it seems to me that what is happening in the US is a cycle of increasing armed escalation. Mass shootings lead to people getting guns for home defence and personal carry. An increasingly armed populace leads police officers to be more prepared for gun violence and more willing to shoot where there is a perceived threat or risk. Increasing police shootings lead to violent protests and 'reprisal' attacks against police. More guns generally means unstable personalities are more likely to have access to powerful weapons, so more mass shootings. And so it goes on.
It isn't a deterrent against local abuses, however well-armed civilians are a deterrent against massive and nationwide attempts (a pure tyranny trying to establish itself, or some foreign invading force).
The societal problem created by unstable personalities is due to... unstable personalities, and unstable personalities tend to boost other's instabilities, a retro-action quickly escalates the problem into major ordeals: the society (armed or not) progressively becomes something else and crumbles.
Someone wanting to destroy/maim/kill will do so (armed or not), and civilians weapons rarely are the best tool for it (check, for example, the Oklahoma City bombing '1995). Arson as a weapon substitute is common, especially in no-weapon zones.
Solving the main causes of tensions (dumb dispositions addicting many citizen to very dangerous drugs, race-related hate, extreme poverty, education and economic conditions letting youngsters leading nowhere...) would reduce the will to destroy/maim/kill.
I don't really think the evidence tells us that armed civilians deter tyranny, in fact tyranny can be extremely effective at suppressing an armed populace. There are plenty of examples of this in the world right now and recent history. Chechnya, Syria (in which Assad is still very much in control), Iraq under Saddam, now Myanmar which is rapidly growing an armed resistance that's laudable, but almost certainly completely futile. There are plenty more. India in Kashmir, Pakistan in Baluchistan. More guns? Easy, just pile on more repression. It works. The only way out of that is a full on militarised civil war with armies and everything, but armed civilians on their own just aren't enough.
Chechnya, on the contrary, clearly showed that armed civilians can deter even a hugely disproportionately powerful invader. During the first war (1994-1996) the Chechen had plenty of good weapons, and kicked the Russian army to the point of winning (they re-took Grozny!). Then the Russians took measures in order cut logistic lines and re-attacked in 1999, focusing on further barring civilians from obtaining weapons and any related material, with a great success (the Chechens had to build inefficient homemade weapons). This is documented, see for example https://reaperfeed.com/5-homemade-weapons-from-the-chechen-w...
The ongoing civilian war in Syria isn't pertinent, as it isn't "civilian vs. regular army" but many tribal factions and armies fighting each other and volatile alliances.
Iraq under Saddam also shows that armed civilians (the Kurds) can resist to a tyrannic government. Others were not well-armed and were indeed crushed.
The rebels during the 1991 uprising could not grab weapons. "U.S. troops that were deployed in southern Iraq defended arsenals or blew up them altogether to prevent the rebels from arming themselves, blocked the rebels from advancing onto Baghdad and even actively disarmed some rebel forces" (sourced at https://en.wikipedia.org/wiki/1991_uprisings_in_Iraq ), in practice killing the rebellion by discouraging it.
Kashmiri separatists are notoriously badly armed, their main approach is a sort of Intifada (throwing rocks)! As far as I know Pakistan gives very few weapons to some subgroups read as not too dangerous for them, and India yells about it but after years and years fails to show serious evidence, probably because there are too few weapons.
> Pakistan in Baluchistan.
Baloch separatists are losing not because they cannot resist, but because their cause is dying as the majority of the population (especially Pashtuns) doesn't adopt it and as the central government concedes more and mode towards decentralization/autonomy.
> More guns? Easy, just pile on more repression. It works.
I doubt so.
> Personally I'd rather put my trust in democracy.
There is no mutual exclusion between weapons and democracy. Switzerland, one of the (or rather, at least IMHO, _the_) more advanced democracy, is shock-full of weapons and has a solid weapon culture.
> Personally I'd rather put my trust in democracy.
That's simply naive. You don't think powerful elites do and will try everything to gain and maintain power over the peasants? Personally I'd rather put my trust in having some way to fight back when the inevitable happens instead of being powerless.
> India in Kashmir
Not sure why you think Kashmir is tyrannical? Your other examples are also flawed. The fights happening in lets say Syria are tribal infighting - similar to gang fighting on a larger scale. Similar to Chicago gangs on a larger scale.
Despite all the flaws of Assad, most Syrians like him. It's the same thing as what happened in Libya or Iraq. Regime change wars is what destroyed those countries thanks to which there's slavery back in Libya.
This has happened several times in history. People get disarmed, then their rights get taken away. The most recent example is Venezuela.
The classic argument stating that tyrants try as early and hard as possible to confiscate weapons from civilians is another cue.
An army pretty much knows the truism stating that occupying is more easy if the zone is gun-free.
There is an often-neglected complement: by the same principle an army fighting against another which occupies a nation usually try to deliver weapons to civilians rebelling against the invader, even if manufacturing and delivering them dissipates very precious resources. It was quite patent during WW2, for example in France where the OSS and SOE parachuted a huge amount of weapons to the Résistance and Maquis movements. In the same vein the German army, during the invasion, quickly confiscated civilian weapons (they were registered) and was then very reluctant to deliver weapons to their local sympathizers (at first and for an extended period they bluntly refused).
An armed (and determined) populace is quite a good deterrent.