But is this really true? Honest question: the recent BTC/BCH split effectively doubled the supply in one single instant. Can't this happen again and again whenever the pressure of demand grows too high?

Can't do that with gold.

But that’s the equivalent of then going to silver or using an entirely different element isn’t it?

How many such "entirely different elements" are there?

> Gold will never be as measurably scarce.

Even with Bitcoin we don't know the exact scarcity because private keys get lost.

A wallet to which the private key has been lost is indistinguishable from the wallet of someone who is holding their funds because they want to save them for the future.

Excellent point. Still, we know that there is not more than a certain number; versus with gold there could be more or less than any estimate.

There's now 2000 cryptocurrencies. Where's the finite property?

It's called PoW. Go for the highest total work in the chain. If you go for anything else you are either allowing your self to be attacked by a malicious branch, or you are yourself attacking the network. There's at any given moment exactly one chain that has the most PoW (by definition). That's the reason why Ethereum is switching to PoS, because they know they can't just take over Bitcoin on total PoW. Be advised that PoS means it's not really a public ledger, but a private chain set up by a very large private club.