Each individual proof is zero knowledge, but downloading a _bunch_ of them is an indicator, yes. There's no real way to work around this with the current ZKP scheme. I'd argue ZKP is, in theory, the least worse option of all current age verification scheme.

My personal opinion is that age verification itself is a bad idea, but if we're going to go ahead with it, I'd much rather we use ZKP for it than the current mess of "upload your passport and picture of yourself to dodgy 3rd parties that likely now have your browsing traffic associated with your real name"...