One obvious problem would be that some cards are good no matter the cost. I'm going to reanimate an Emrakul even if the card costs 40 mana. Manaless dredge will still be manaless.

In some formats, this would be an excessively obtuse ban list. Obviously oversimplifying, if anything with mana value 4 or higher is utterly unplayable in Modern, any popular cards that "price out" is effectively just banned. People are playing Llanowar Elves to hit 3 mana on turn 2 for a Stone Rain or something. If the price of either changes, whether up or down, that just kills the point of trying to play them.

Could this work in a game that's explicitly designed around live market prices? Yeah, I'm sure NFT games are ready for their comeback :P.

And now, I present without comment that time Valve tried dynamic pricing in Counter-Strike: Source and people could spam buy cheap guns until the server crashed.

Are you familiar with the MTGO format Penny Dreadful?

Basically, any card that was worth $0.01 or less in the preceding season is legal in the current one. It's an interesting system that, in practice, works similarly to what you're proposing, except with a ban list rather than mana cost. The cards aren't likely to fluctuate in price based on external influences (it's rare that a $0.01 card becomes such a breakout hit in another format that its price goes up, though it does happen on rare occasion) - usually it's the Penny Dreadful format itself that causes those market fluctuations. If a card is popular enough in that format that it starts seeing heavy play, the price often dips up above $0.01 and it becomes illegal in the next season as a matter of course.

The rough analog to what you're proposing would be making any card that saw more than a specific percentage of play banned, but if you're determined to use mana costs, you could (hypothetically, not practically) increase all mana production and costs by a factor of 1000 (so a basic forest taps for 1000x green, and a llanowar elf costs 1000 green), and let costs fluctuate very slightly as a result, but it wouldn't functionally change much. Spending (the equivalent of) 0.942 of a mana on something isn't functionally different in almost all cases from spending 1 mana on it. By making prices only fluctuate on fixed intervals, say, weekly, you'd and only take play within the past, say, 2-3 weeks into account when determining cost, you'd be able to reach equilibrium while also not necessitating frequent deck changes (certainly not match to match).

I don't play Magic—or any TCGs, but I thought this was interesting and had done feedback on the idea. I don't have the experience necessary to weigh in on the substantive question of whether it's a good idea or not, but I do think the logistical issues you raised would not be nearly so problematic.

A big drawback is that your deck's costs can change over night (or even between consecutive games)

You would at a bare minimum not change the costs for players in a tournament in the middle of the tournament. And now generally, I think rather than dynamic cost changes, you would probably be better off doing seasonal patches like a video game's balance. Maybe that's monthly, maybe every 3 months. But certainly not every day or even every week.

It's also only contemplable in digital versions, where a server can monitor every card drop

Not necessarily, though that would make it much easier. You couldn't count every single casual game anyone plays, but for games with a certain level of formality or weight to them you could borrow from chess. In chess games that don't have a very tight time control, players write down both their and their opponent's moves every turn. These are then compared to ensure they match, and fed into global chess databases. It works well in chess because of the convenience of chess notation, but aside from some difficulties with the length of card names it could easily be brought into a TCG.

But separate from that, you may not even need that level of granularity. Wouldn't someone merely putting the card in their deck to play be sufficient? Registering what cards are in your deck is, I believe, already a thing in other games' tournaments. Does Magic not do the same? Because that should be sufficient, at least in the highest level of play, to determine whether players have the intent to use a card because they believe its value is appropriate or cheap.

Personally one of the things I like about MTG is that they primarily ban cards as a solution. Other games change rules, have errata, or simply remove cards from existence. Banning cards maintains the functionality of both the game and card. It enables discussion about banned cards coming back, you can have no ban list tournaments, or even try gauntlets of banned cards to better understand them. Changing the text of the card makes that impossible, digital only card games can just remove the card from your collection, and discussing which years' ruleset to use as a group is way harder than agreeing on a banlist. Especially for a game like MTG which has new cards coming out almost every other month, I think it's the best way for designers to push boundaries but still let players dicuss their decisions

Actual arguments aside: capitalism doesn't magically produce the results that its proponents say that it does and introducing it as a solution almost certainly never produces the intended results. Unless the intendes result is "one asshole figures out how to game the system and make it worse for everyone who isn't him." Which unsurprisingly, is not what I want from my card game