When you compare the price of cards to basically any other sports collectibles, the pricing does not seem to make any sense.
It could be that over time vintage bats will go up in value, but comparing it to cards may not be a useful way of thinking about it. The number of people who shift from collecting cards to collecting other kinds of memorabilia is not tiny, but it is also not a huge number. And so each has its own, largely independent market with (largely) different populations which drive demand.
I think many memorabilia collectors feel like what they collect is a "better deal" than cards of the same players. I look at my collection and find it hard to believe I can own the original contract that Roy Campanella signed with the Dodgers (as one of the first black players to sign with an AL/NL team) for a tiny fraction of what a high-grade (PSA 9) Campanella rookie card goes for even though there are far more PSA 9's and 10's than there will ever be original copies of the contract. At the same time, the market of people who are looking for the card far surpasses the number of people looking for the contact, even though I would argue that the historical significance of the contract far surpasses the card.
All that said, I think vintage bats are some of the coolest items in the hobby, and could definitely see an increase. I'm just not sure whether comparing them to cards is a way to consider the question.
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