This isn’t black and white. There’s a medium between:
* Wait for 10 years of cryptanalysis (specific to the final algorithm) before using anything, which probably will be relatively meager because nobody is using it
* Expect the standardization process itself to produce a blessed artifact, to be set on fire as a false god if it turns out to be imperfect (or more realistically, just cause everybody a bunch of pain for 20 years)
Nothing would stop NIST from adding a post-competition phase where Google, Microsoft, Amazon, whoever the hell is maintaining OpenSSL, and maybe Mozilla implement the algorithm in their respective libraries and kick the tires. Maybe it’s pointless and everything we’d expect to get from cryptographers observing that process for a few months to a year has already been suitably covered, and DJB is just being prissy. I don’t know enough about cryptanalysis to know.
But I do feel very confident that many of the IETF standards I’ve been on the receiving end of could have used a non-reference implementation phase to find practical, you-could-technically-do-it-right-but-you-won’t issues that showed up within the first 6 months of people trying to use the damn thing.
I don't know what you mean by "kick the tires".
If by that you mean "perfect the implementation", we already get that! The MLKEM in Go is not the MLKEM in OpenSSL is not the MLKEM in AWS-LC.
If instead you mean "figure out after some period of implementation whether the standard itself is good", I don't know how that's meant to be workable. It's the publication of the standard itself that is the forcing function for high-quality competing implementations. In particular, part of arriving at high-quality implementations is running them in production, which is something you can't do without solving the coordination problem of getting everyone onto the same standard.
Here it's important to note that nothing we've learned since Kyber was chosen has materially weakened the construction itself. We've had in fact 3 years now of sustained (urgent, in fact) implementation and deployment (after almost 30 years of cryptologic work on lattices). What would have been different had Kyber been a speculative or proposed standard, other than it getting far less attention and deployment?
("Prissy" is not the word I personally would choose here.)