I think the general idea is quite interesting. There are some card suggestions worth considering here. Balance is often an issue, though. With self-synergizing cards you have to carefully think about how strongly and reliably their "in games using this" clause affects their actual power. These considerations should be reflected in the card cost. I'll take silverspawn's suggestions as an example (hopefully, I'm not erring on my own):
Action - 5$ - ?
Reveal your hand. +1$ per card revealed.
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In games using this, during your cleanup phase, you may draw 6 cards instead of 5
A terminal Platinum for $5? This would elevate Big Money to new splendour, to the point of ridiculousness. Probably more accurately priced at $7, if Bank is any indication. The effect below the dash is interesting, though. I just think the self-synergy here is too bland and powerful.
Victory - 14$ - ?
Worth 10 VP
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In games using this, other Victory Cards are worth half as much as normal (rounded up)
It seems overpriced, but I really can't tell how much it should be. Bu I'm pretty sure this is not a very intriguing concept overall.
Action - 2$ - ?
+1 Action
+1$
Trash a card from your hand.
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In games using this, whenever you trash a card, you may draw a card
The way you phrased it, this is very close to a Junk Dealer, maybe a little worse, so it should be worth $4, I think. The big issue with this is imo that it makes many trashers too powerful, because both trashing and card draw are a huge deal. "In games using this, whenever you trash a card, +$1" would not as strong but still worth going for, at a cost of $3 perhaps.
Action - 1$ - ?
+1 Action
+1 Card
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In games using this, whenever you play an action card with the same name as any action card you have in play, +1$
This turns cantrips into Peddler+ cards, which MIGHT be okay by itself (not sure here). However, the once again blatant self-synergy makes this card akin to a Conspirator-Peddler that enables copies of itself, so I'd price it at $3.
Another idea from scott_pilgrim:
Maybe something like:
Action - $4
+2 buys
+$2
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In games using this, all cards cost $1 less, but not less than $0.
It has obvious synergy with its bottom-half, but is still neither strictly better nor strictly worse than any existing cards. (I think the bottom half would work fine on Woodcutter, but given that Woodcutter already exists, this has to be different from Woodcutter in case they appear together.) It also mostly satisfies LastFootnote's suggestion that it shouldn't create opportunities for players to break rules (though this fails with a few TfB cards, for example, players may accidentally draw an extra card with Apprentice). It does suffer from having its rule continue to persist even when the pile is emptied and it's no longer visible, but I don't expect the pile to empty very often.
I think this card is
strictly usually better than Bridge on its own (EDIT: if bridge is not in the kingdom). Yes, the effect is not stackable, but rarely would you play many Bridges in the same turn. It's also not TR-/KC-able but these ae exceptions. In most cases, it's better than Bridge, and too powerful or $4.
Another issue you pointed out yourself; it applies to this style of card in general. There's no real help for considerations with TfB cards here other than to constantly keep this in mind. This might become annoying. More so, it throws balance for many cards out of the window. Consider opening buys, especially with 4/3 which turns into 5/4! This could be fun but it might as well break the game entirely.