The US does not have contactless credit cards. Britain has a financial and national security interest in American tourists — who will need oyster cards.
I have 2 Mastercards and 1 Visa. Only one of the Mastercards support contactless. The one without foreign transaction fees doesn't. It's also been vary hard to find a chip+pin card (without an annual fee) instead of a chip+signature even though it's been around for what, 20 years now?
In general even if the card isn't contactless, a decent phone, which can perform contactless transactions, can be hooked to the same account anyway.
In fact I deliberately own a non-contactless credit card (from my good bank, who were happy to send me the non-contactless version when requested even though their default is contactless) and then enrolled that card in my phone so the phone can make contactless purchases.
Thus, my credit card can't be hijacked to do remote purchases because purchases with the card require a physical connection, and yet I can make fairly large card purchases contactlessly, because my phone vouches for them after I unlock it.
That is true, but even with a US card in the US, there are vague scenarios where ApplePay requires a signature[1]. So it's problematic using it for unmanned terminals when traveling. I've had trouble traveling internationally and wouldn't trust it taking mass transit without extra time or a backup option.
Obviously TfL can't do anything about a US bank/ card issuer having policies that lose them money, but the turnstiles are aware that they have no (passenger accessible) inputs and so they do not ask for a signature.
EMV lets the card (or in this case maybe a phone) and the terminal (in this case a turnstile inside the station, or a reader on a bus) negotiate what to do, the issuer may not be involved since it's possible they'll agree the entire transaction needn't yet involve the issuer. This is related to one bug in EMV, you could intercede in the middle to tell the card "It's OK, no need for a PIN" and also tell the terminal, "Yes, the PIN supplied was correct" and since the terminal doesn't know the correct PIN you've now got a shim that allows you to use the wrong PIN with a stolen card†.
Anyway, TfL terminals aren't going to agree to signatures. So, if your card really does only work with a signature then you can't use the turnstiles, along with presumably many other modern conveniences.
† There are obvious technical fixes. But the fixes cost money, and fraud is a cost banks can pass to their customers, guess what happens next.
