Speaking from an engineering perspective, this is part of the reason I've never been comfortable with warrant canary or "extra-warrant" compromise canary.
Let's say you run some kind of service for which you offer privacy/security assurances, but, at some point, you're compelled in some extra-warrant way to violate those assurances. Or you're simply compelled by warrant, while also being compelled not to implicitly signal that by canary. Or you discover a compromise, previously without your knowledge, and are compelled not to disclose it.
I could easily imagine that many of the same official powers (public or secret), or de facto powers, that would enable the compelling wouldn't see the legal arguments of some lawyers as showstopper barriers to keeping the canary intact. If you think that kind of scenario is plausible, then touting a canary is arguably doing a disservice, from the start.
At least half of engineering is honesty and specification, so the introduction of a canary, in an environment in which you can't be sure you can comply with it, and perhaps can't disclose when you realize you definitely can't comply-- doesn't seem like good engineering.
If we're not sure we can honor canaries, then perhaps it's better not to do canaries at all -- and perhaps to instead specify our assurances better, including broad exceptions we anticipate we can't cover. Maybe lawyers and C-suite ultimately determine it makes sense to qualify the assurances with language like, "conceivably could be compelled by [particular government where company is based]" and "conceivably compelled not to disclose".
Personally, some of the hypotheticals are way outside my expertise (and stomach), and I'd rather focus only on engineering good solutions. But canary-type situations and assurances sometimes involve engineering, and sometimes we can foresee potential future problems that we should discuss with the appropriate people in our organization, before it becomes a problem. Then, hopefully we work with people who use all the information, from engineering and other sources, to do the best thing.
(BTW, I'm in the US, and I think, for example, that a practice of warrants is a very good thing, in principle, and I have some trust in the mechanisms and checks&balances of our system. I appreciate that different countries and people have different situations and perspectives, and that things are very complicated and imperfect, even in my own country.)