Be sure to keep in mind that removing a card limits the overall possibilities the game has to offer, and thus, risks simplifying strategy. There's a tradeoff though, when something offers a lot of swinginess, but not a lot of strategy, it hurts the game more than it helps. The best example I can produce off the top of my head is "items" from Super Smash Bros. which are unanimously banned from tournament play, because although they provide unique effects with interesting strategic implications, they make best of 3 sets far less accurate and hurt enjoyment more than they help. (Actually, some of the items are less like 2/5 Mountebanks and more like Harvests, but that particular community found life easier if they threw the baby out with the bathwater).
These are the cards that I think I would remove from Base. To keep the question simple, I'm not going to allow alternative replacements, thus, for me to say I think the game would be better off without a card, it has to be so bad that I don't mind it skewing the color and icon balance of the age.
1. Oars
The problem with Oars isn't that it's a bad card, although it is. The problem with Oars is that it is a bad opener. It has a useful niche and is an interesting dogma to consider later in the game, but it if it is in your opening hand, it really screws you over. While it does have a niche, the niche is still weak, and not all that interesting. It's not worth the swinginess that Oars produces by screwing over opening hands, hands like Archery/Oars, Oars/Code of Laws, Oars/City States. The other half of those pairs either are doing more to not suck as openers or have a more interesting niche, Archery does what you wish Oars was doing later in the game, Code of Laws is a very interesting card and can tussle for early icons, and City States has a good niche and even isn't that bad in the opening - though it's a lot worse in the opening if your opponent can notice that your opening two cards are City States and Oars, and proceed to refuse to get a 4th tower so that you are starved out of having any good dogma at all.
2. Oars - This is sort of a joke but.. Metalworking. That card is really swingy in a silly way. People have posted the turn 1 Monuments and stuff. The nice thing about removing Oars, the way I've made up these rules, is that it nerfs Metalworking just enough to make Metalworking tolerable. It is enough to keep Metalworking off the chopping block.
That's all I have for you. I wouldn't remove any other cards. As I gain more experience perhaps this list would grow.
This might seem like a dumb thread, but, whatever, I had fun making it.