My only real disagreement so far is that Advisor is either slightly or way too high. The card is terrible.
Advisor can be really good; you need a lot of them.
I challenge you (or anyone reading this) to post one log where Advisor was "really good"
If your deck is homogeous enough (e.g. Advisor/Masterpiece) then it draws two OK cards and discards an OK card.
The only situation I can think of where my deck is more or less homogenously filled with OK cards is either Trader/Feodum or Masterpiece/Feodum (and things like Hamlet/Watchtower engines, but then you certainly don't need Advisor). However, in those games I do not want to waste a $4 buy on anything besides Trader, Feodum or Silver.
Otherwise, if you are drawing your deck anyway, it doesn't matter what they discard.
You can't draw your deck with Advisor, so if you are drawing your deck anyway you most likely have other means to draw, in which case your example mistakes the power of those other draw cards for that of Advisor. An exception might be if you have lots of spammable cantrips (Hamlets, Peddlers) or some sifters (Cellar, Warehouse), in which case having a bunch of Advisors isn't as bad as it usually is. Those situations, and the ones you list at the end, are why I'd rank it #197 instead of #204.
Another thing is situations when you want to draw bad cards to trash them; Count and Forge let you trash a lot of cards at once, and a bunch of Advisors let you draw almost everything you want to trash, instantly powering up your Advisors.
You first have to get a bunch of Advisors over other cards, and getting a bunch of bad cards in order to slightly facilitate the trashing of other bad cards sounds like a crappy idea. Besides, if you play multiple Advisors in a row, you are more likely to have your Forge/Count discarded than you are to have it in your starting hand, so you are left with all your junk and no means to trash it.
Even in the opening, you can play the "do I have my Chapel this hand?" game.
Whether you trash 3 or 4 cards early on is insignificant compared to your opponent potentially discarding your Chapel, which can be game-deciding.
Then of course there are situations where you literally don't care what else in your hand; Secret Chamber/Storeroom/Vault, Cellar discarding exactly as many cards remain in your deck (Cellar/Counting House-style). Double-Tactician/Vault generates $9 per turn without assistance, tack on two Advisors and you can get a Colony; Secret Chamber/Storeroom works for Provinces with just one Advisor.
Yes, but even here note that it only offers slight support, and is not a key card. Compare this to Secret Chamber, which can be an absolute monster in sufficiently trimmed Scrying Pool-engines, yet it's still ranked #196. My point is not that the card doesn't have its uses, but that it's often terrible, rarely good and never great.