But that's not really a helpful answer for what you asked. Cards to consider excluding for weakness (with the caveat that you'll miss out on those rare shining moments they have):
-Harvest-- top of the list for sure
-Transmute
-Counting House
-Navigator
-Fortune Teller
-Beggar
-Pirate Ship
-And obviously any of the cards cut out of base and Intrigue for being too weak
What about Mandarin? Without Capital on the board, it never seems attractive.
Maybe Dutchess? Possibly Fool just because it's so awkward?
Not saying these are good, but both have niche uses.
Mandarin is good tactical buy on some Colony or Dominate boards. Top decking Plats this way can well be worth it as the VP differential is pretty high between a Duchy now and a likely Colony next turn. Less commonly, it can be clutch for something like Vineyards with a +buy to make sure you grab something next turn. The best case scenario for this is something like Hop - GGSHop or similar can use Mandarin to top deck a Prov hand each turn. I will, very rarely, consider burning a $5 for something clutch like replaying two Idols to give out the last curse. I have not tried enough, but he might actually combo with Goat enough to merit buying him more to more reliably feed the Goat. With deck tracking, he can be an absolutely clutch buy to hit an early Lamp/Wishes.
Mandarin is also useful for times when topdecking has very high value like Tournement, Moat/attacks, Pool/City quarter. It is just a highly gimped Count in this case, but that still is worth it if it is clutch to either have something in your hands between your turns or if whiffing is enough of a VP differential that overbuilding is worth it. He pairs well with Mystic, but competes at price point. With multiple plays, he is very good with Wwell, Herald, and a few other such things.
What hurts Mandarin is that if you are not using his on gain or top decking as something valuable for your deck, his space efficiency is worse than Silver - as a terminal action. That is harsh. He can let you smooth your cash points a bit ... but for $5 he is very weak if your deck has not real use for top decking or treasure recycling as such.
Duchess is most useful in games where gainers are absent. Duchess can let you gain fodder for a some big Tfb like Altar so you can keep use the trasher after your starting dross is gone. If you are still engine building you have to sacrifice a $5 gain now for two $5 gains later - not often a good bet with the three turn lag ... but actually useful once you want duchies. She is more nichely useful when actions are useful as such - Pool/discard for benefit, Sacrifice-as-only-village, and Gravedigger. More often she is useful to do a three pile (e.g. Duke/Duchy/Duchess, Igg/Duchy/Duchess). The terminal spy power is mostly useless, but a cheap terminal silver can be useful in all the places you would expect - Lib, Wt, Menage, Diplomat, etc.
Fool is an abysmal card. First boons swing wildly to start with, second Fool order often means that one player gets 5/6 boons to the other player's 3 in a shuffle. He would have been far better off with a mechanic where you are "found" from the woods if you discard the Fool without playing him.