>and when you ban people, you kinda give them power.
The key word being "kinda". You give the perception of power, but there are plenty of things in society we deal with by a form of "banning" (such as incarceration) in which we judge the ban to be good regardless of the power it gives people, or the ideas they represent or practice. Locking up child abusers, for instance, may give the spectre of child abuse power, and highly-publicized instances may fuel the moral panic around "strangers out to get your children", but that doesn't mean they should not be locked up.
In civil society, we are justifiably afraid of many ideas - I don't know anyone who wouldn't be afraid of a Nazi-style dictatorship, or its prospect. Fear can be a legitimate way of preventing bad things from happening. I fear dying in a house fire, thus I take certain precautions when cooking. In the same way, a demonstration of power over a person or idea may outweigh the power supposedly given to that idea by banning it.
The key is a balance; it may well be that you get an instance of the Streisand Effect, but it has to be shown that the consequences of that outweigh the very material consequences of such ideas coming to fruition in real life. For example, many people don't know who Barbara Streisand even is, and if they do, they likely don't know about the pictures of her house. The very canonical example of the Streisand Effect shows a short-lived controversy about the actual matter and ensuing attention for a few months after the incident. Then people forgot, or simply stopped caring. "The Streisand Effect" is more of a Streisand Effect than the actual incident that created it.