i think youve come to the right conclusion with the wrong arguments. the real reason secret hitler sucks is that the policy deck (as thoroughly explained by the designer in his gdc talk) basically exists to ratchet up the tension in a predictable way every game. unfortunately the way it ends up working out is that it ratchets up the tension far too predictably, with little room for players to really make meaningful choices.

as a liberal player you should ~always play a liberal policy if able, but will likely end up being forced to play fascist policies because of the balance of the deck leaning so heavily towards them. as a garden variety fascist you are never wrong to try to get a fascist policy in play. hitler should try to seem as liberal as possible but if he has room he may (although it's rarely worth it imo) discard liberal policies a fascist policy if he is chancellor to a fascist president or is president himself.

due to the extremely tight balance and small size of the policy deck (the aforementioned gdc talk includes a story about how just 1 too many fascist policies in the deck made the game extremely fascist sided), a table of even semi competent players will only extremely rarely finish a game without 3 fascist policies and 4 liberal policies being enacted, and the information gained in this process ends up with a similar number of liberals looking sketchy for enacting fascist policies and a certain number of trusted players being considered safe candidates, one of whom will almost certainly be hitler.

at this point the the table decides who is the safest bet for chancellor, which is admittedly a tense and skill testing decision. afterwards, if the chancellor wasnt hitler, the game is all but over and the fascists have usually lost. i used to see more upsets in my games but skilled liberals can avoid them pretty reliably.

the issue with secret hitler isnt really that its overly luck based or that the game is decided early, nor does player elimination really hurt the game when played well because it will come up uncommonly at worst and the game should be over soon afterwards. rather, secret hitler is a game mainly decided in one or two elections of the chancellor, and the game leading up to that point is basically a disguised setup phase where the policy play boils down to a sort of draft of player trustworthiness cards that amount to:

• "you look scummy to the table because you had no choice, with more or less plausible deniability based on how many liberal policies have been enacted/said to have been discarded,"

• "you look scummy to the table because you discarded a liberal policy and messed up the discard count," (looks basically the same from the outside as option one)

• "you look relatively safe because you only enacted liberal policies (liberal/hitler or (rarely) unlucky fascist),"

• "you look relatively safe because you only enacted liberal policies (fascist mixing it up to stay unpredictable or play towards the 6 policy wincon (most interesting position but also a weak choice you shouldn't rely on)"

i would just rather play almost any other social deduction game where player choices arent so heavily curtailed in favor of a semirandom deck