A typical situation is that there's a contentious issue, and some anecdotes reach your attention that support one of the competing hypotheses.

You have three ways to respond:

1. You can under-update your belief in the hypothesis, ignoring the anecdotes completely
2. You can update by precisely the measure warranted by the existence of these anecdotes and the fact that they reached you.
3. You can over-update by adding too much credence to the hypothesis.

In almost every situation you're likely to encounter, the real danger is 3. Well-known biases are at work pulling you towards 3. These biases are often known to work even when you're aware of them and trying to counteract them. Moreover, the harm from reaching 3 is typically far greater than the harm from reaching 1. This is because the correct added amount of credence in 2 is very tiny, particularly because you're already likely to know that the competing hypotheses for this issue are all likely to have anecdotes going for them. In real-life situations, you don't usually hear anecdotes supporting an incredibly unlikely-seeming hypothesis which you'd otherwise be inclined to think as capable of nurturing no anecdotes at all. So forgoing that tiny amount of credence is not nearly as bad as choosing 3 and updating, typically, by a large amount.

The saying "The plural of anecdotes is not data" exists to steer you away from 3. It works to counteract the very strong biases pulling you towards 3. Its danger, you are saying, is that it pulls you towards 1 rather than the correct 2. That may be pedantically correct, but is a very poor reason to criticize the saying. Even with its help, you're almost always very likely to over-update - all it's doing is lessening the blow.

Perhaps this as an example of "things Bayesianism has taught you" that are harming your epistemic rationality?

A similar thing I noticed is disdain towards "correlation does not imply causation" from enlightened Bayesians. It is counter-productive.