The canary in the coal mine is only useful because there's only one plausible explanation for it keeling over. If they died all the time for no good reason they'd be useless. It might be really cool if we could extract signal against a noisy background but there's mathematical limits on our ability to do that even in theory, and we're generally better off looking at the less noisy signals.
Plus chasing noise turns out to be really dangerous. 5% of the time or so, random processes will correlate with something else you look at with 95% confidence. Your suggestion is not a good idea at all, it's a recipe for spurious connections and wildly disproportionate responses, no matter how good it feels to a human brain.
Except that when it comes to mass animal deaths, the rate of it being caused by human activity isn't anywhere near as low as noise. And mass die offs simply don't happen "all the time". Canaries die of non-gas-related causes far more often than entire flocks of birds and schools of fish die within feet and seconds of one another.
Essentially, if a mass die off doesn't correlate with a particularly sudden weather event, or known human activity (fireworks displays) it's safe to assume it is us, from something we (tautologically) didn't know was happening or didn't expect to cause these problems.
And at that point, it's just straight-up good science to investigate the remaining cases to better understand our environment and how our activity is affecting it.
Plus chasing noise turns out to be really dangerous. 5% of the time or so, random processes will correlate with something else you look at with 95% confidence. Your suggestion is not a good idea at all, it's a recipe for spurious connections and wildly disproportionate responses, no matter how good it feels to a human brain.