If you're doing non-redundant tests and your uncertainty bars aren't shrinking, it's usually a skill issue.

If it looks like a duck, it might be a duck - or a painting of one. If it looks like a duck, swims like a duck, and quacks like a duck? The joint duck estimation is much more confident now. There might be a few more observational tests one should administer before committing to a duckhood decision, but each tests pins down variables and rejects confounders. Uncertainties are cut down, and we get closer to crossing the threshold between "duck-informative" and "duck-actionable".

Thus, it's often worth it to improve observability. If you managed to make a certain test more reliable, or cheaper to administer, or reduced the chance of adverse effects? Or, in other words, improved SNR, reduced costs, and reduced costs? You can get more information for your buck. Paired with good knowledge: you can make better decisions more easily.

The fact that the thought of "having more information might be bad actually" even occurs in the field of medicine shows just how far it is from being optimal. Having more information isn't always beneficial - some information is genuinely redundant. Some information is not worth the effort of gathering and integrating it. But if you get more information and it results in worse outcomes? You're doing something wrong.