Then all that happens is we adopt those other schemes faster, spot the holes faster[....]
I agree, and I'd argue we don't go far enough yet. We should adopt a few of these post-quantum schemes now alongside a trusted but quantum-vulnerable protocol such as RSA.
You ensure that communications are safe unless all schemes can be broken. Here's how. Most public key cryptography is used to send a roughly 128 to 256 bit long one-time use key for a symmetric cipher like AES. It would be possible to select, say, 5 different public key protocols: 4 new (and therefore perhaps flawed) post-quantum schemes plus one quantum-vulnerable but trusted protocol like RSA. Generate your AES key, then generate 4 random bitstrings of the same length. Then, using the 5 protocols, use the first protocol (RSA) to securely send the key XORed with the 4 random strings, and use each of the other 4 protocols to securely send one of the random keys. An attacker who can crack any 4 of the 5 protocols cannot obtain any information about the key.
The upside to this is that if you take a diverse set of promising strategies for post-quantum public key crypto from several agencies that don't trust each other, chances are there will be at least one that's OK. Even if none of them work well, you're still no worse off from a secrecy standpoint than with plain RSA.
The downside is that keys will become longer (many post-quantum algorithms need many kilobytes) and computation will be more substantial. Practically, that means you won't want to ever have to read your public key to someone over the phone (but you could read them a hash of it - almost as good), and tiny, frequent crypto-protected payloads would see an increase in CPU utilization, but there would not be as much of a change for long payloads where the cost of the public key handshake to transfer the AES key is amortized over much more data.
With computation becoming faster, and with the Internet increasingly carrying data that may be sensitive even a few decades in the future, we should start using quantum-prudent methods defensively ASAP, especially since the downside is negligible already, and it's shrinking with Moore's law.