No, Militia can't lock you out of the game. Maybe Militia+some other combination of cards can, but just Militia can't lock you out of the game.
You mean Miltia plus Witch? Like Followers, the card I actually talked about? That card can indeed lock you out of the game or make it very unpleasant in some Kingdoms. Doesn't mean that it is broken though.
This is not fun and is also not a necessary part of the card, even if it had the most obscene requirement to obtain the Banshee locking people out the game is never fun and so we don't have to look at Marsh to conclude that that effect on Banshee is a bad idea. To reiterate, it isn't a case of it being too powerful, it's a case of it being un-fun and easily fixed without changing the concept of the card.
I think that Cultist games are unfun because it is so ridiculously overpowered and junks quicker than anything else.
I think that a 5/2 opeining in a Kingdom with e.g. Mountebank and Monastery is unfun as the game is already over before it started.
Dominion has, like every game, numerous issues and in my limited experience with two Debt attacks (Asper's Scribe and my Blackmail) I did not find them to be game-breaking.
About partial analysis, about ignoring one part of the pair, I already said everything about why you cannot do that. It'd be like looking at Mercenary and concluding that a card that draws, yields Coins, trashes and Militias is totally bonkers while ignoring the path towards that very non-Supply card.
Mercenaries would be ridiculous as a Kingdom card. But it works as a non-Supply card as you have to jump through some hoops to get it. Unconditional Debt attacks are something you shouldn't do or at least be careful about. Here the condition of handing out the Debt is that you previously helped the opponents to thin.
If attacks are stronger in 3+ player games anyway then how is having the non-attack part of the card get stronger with more players a good idea?
Tell that to Pirate Ship and Jester, why don't they just target one player? Why is Pirate Ship so risky in 2P and so safe in 4P? Why can you only gain one card with Jester in 2P yet three cards in 4P?
Why is Ambassador a net trasher in a 2P game yet a net junker in a 4P game (assuming for the sake of simplicity that every plays has an equal amount of Ambassadors)?
I don't see anybody here ripping apart such official Attack cards whose power and behaviour varies significantly with increasing player count.
Does the card really get ruined if that part is just changed to a flat +1 or 2 Coffers?
No, here I am totally with you. As I already said in the post you replied to, I think that an unconditional
+1 Coffers is good as it gets rid of "Coin spread" issues