It's not really a more technical explanation. I get how localstorage and cookies are different. But it's a technicality the user doesn't care about. The problem is third party cookies.
Self-hosted solutions where only the site I visit tracks me is not a problem even for me as a privacy extremist. But calling it "no cookies" and putting the id in localstorage is misleading or misunderstanding the problem people have with cookies in the first place.
Don't get me wrong I like the effort and was looking for something similar before just implementing my own solution with regular nginx logs. But this is a space where trust is important.