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Anecdote isn't worthless, it just takes a lot of it to become credible.
Like, think of an anecdote like a single study - doesn't carry much weight, but may indicate that further investigation is called for. A shit ton of anecdotes all making a similar claim - now we've got peer review that may actually add up to something significant. It also may not, but the more it builds momentum without being debunked, the more likely it is to be actually getting at something real.
On the other hand, when someone claims something is impossible/something has never happened before/something happens every single time, but you have just 1 anecdote from a credible source that contradicts that claim, then that 1 anecdote is enough to know that they are wrong.
Example: some pundit states: our government has never executed an innocent man. You just need proof that they have executed a single innocent man to show that the pundit has no credibility on the subject and that it's thus not an impossibility that other executed men were also innocent.
Doesn't a "lot of anecdotal evidence" eventually become a sample set?
Not unless someone methodologically captures all the accounts through interviews and surveys and turns it into one.
I agree that anecdotes aren't worthless, but for different reasons. There's actually a saying that goes, "the plural of anecdote isn't data." Anecdotes are just stories. They aren't data points and they aren't peer reviewed. If you want to turn anecdotes into data, you have to do the proper interviews and surveys to actually build a dataset and then get the peer review, but at that point we aren't talking about anecdotes anymore.