If you take a quantitative, cost-based approach to modeling security through adversarial capability, obscurity becomes a perfectly valid security measure if it's not used in isolation. We don't use it for cryptography because the tradeoffs aren't worth it. It's better to design cryptography with provable security based on mathematically rigorous computational hardness assumptions than it is to make secret algorithms.

In the context of application security, if the decision to obscure some or all of your system incurs a non-trivial cost to an adversary, it makes sense. We can't rigorously and mathematically prove the security of applications in the same way we can prove e.g. an algorithm is sub-exponential instead of polynomial time.

You often see "security through obscurity" mentioned in the same way that people cite "appeal to authority" or "ad hominem" fallacies in internet debates. The reality is more complex than that. Fundamentally, anything that increases the effort required by an adversary to successfully compromise your system is worth considering. You just shouldn't depend on it in its entirety. Closed-source software is a good example of robust security through obscurity, as basically any security engineer will tell you (I'd rather look at source code line by line to find vulnerabilities than try to find them through trial and error in a penetration test).

The trivial counterexample is that all modern crypto techniques rely on keeping a key, or part of a key, secret. That's security through obscurity, and you've just stated bluntly that obscurity never works under any circumstances, right?

What you want to do instead is talk about tradeoffs. Talk about how much information you need to keep secret in exchange for a given window of effectiveness, and state a preference for systems which provide longer windows of effectiveness while requiring less information (such as only a key, or part of a key, instead of a key and an algorithm) to be kept secret.

Also, take care with your argument about "pre-modern crypto techniques". Some of them remained effective for centuries after being invented, which is a far cry from your "cannot be argued that they worked", and not necessarily a favorable comparison with many modern techniques, which are lucky if they make it a couple decades before being broken.

(also, of course, all cryptographic systems eventually get broken, which is why every so often we switch to new algorithms, longer keys, etc., and you seem to be arguing that any system which eventually gets broken is a system which never worked, and that's also wrong)