If IP addresses didn't matter for privacy, Tor routing wouldn't exist. If IP addresses weren't useful for blocking specific users, IP bans wouldn't exist. If IP addresses weren't useful for tracking, operators wouldn't have gotten up in arms about Apple's private relay service. Obviously this stuff matters.
Remember that not everyone lives in or around San Francisco. For someone in a suburban/rural area, an IP address combined with things like timestamps, user ids, and the text of the edits can go a really long way towards unmasking them. Even for people who live in more urban areas, it is still obviously easier to find someone who lives in San Francisco than it is to find someone who could be living anywhere on the West Coast. If they could also have been using a VPN, or time-shifting their posts... that makes it even harder.
In contrast, how hard do you really think it would actually be to get some address data from a voter roll or via a warrant or even just through one of the scummy person lookup services online and to iterate through everyone who shares that IP address and check to see how many of them are named Pietri? Or who have shared the username wpietri across another account, or posted somewhere else at roughly the same time? Your IP address is drastically reducing the search-space for other attacks, many of which (timing, text-analysis, etc) are impossible to get rid of when making a Wikipedia edit.
But for the current context, where we are talking about whether or not user account registration is helpful in preventing abuse, I think the kinds of low-probability, long-timeline consequences you describe are not really going to deter most would-be vandals. Especially since Wikipedia is going to know the vandal's IP address whether or not it gets show publicly. So I think Wikipedia is still a good example of how "no user accounts" is workable at scale.
Anyhow, that seems besides the point. All HTTP requests come with IP addresses. That the police might be able to trace them back to a house eventually does not say much about either Wikipedia (who would give up an IP address with a warrant whether the edit was for a named account or an anonymous one) or no-user-account systems in general.
They describe it as an anonymous payment system. That matches the first definition here: https://www.dictionary.com/browse/anonymous