Why would they need Chainalysis? Is this just a UK thing? In US Kraken sells monero, which has limited to no chainalysis in theory; clearly it must not be a regulatory requirement.

No country has it as a specific regulatory requirement. In the US it is vaguely called maintaining an “adequate compliance program.” Blockchain analysis software is likely to be considered an important part of a compliance program by the government, especially when they are in the middle of a crackdown and new DoJ guidance is big on prosecuting this kind of thing (especially prosecuting individual compliance officers for AML failures). Pretty sure Kraken allowing XMR is a source of tension between them and governments too.

This all seems bizarre to me. I could go buy gold today with cash, melt it down to remove the serial numbers, and no one would have a fucking clue where it came from or where it is going. And it'd be way more reliable as a store of value and easy to exchange anonymously across borders.

You have to file export declaration when moving more than $2500 of anything out of the country (except personal stuff for vacations or whatever). You also have to declare gold when you enter if it's over a certain amount. Vague rules in the CFR (https://www.law.cornell.edu/cfr/text/31/1020.210) based off vague laws from the 70s and 80s are the basis of billions of dollars in fines collected by the government every year. This vagueness makes it possible for them to continually shift the goalposts without an act of congress, i.e. what passes for a bank compliance program in 2023 is much different than what passed in 2005 even though none of the underlying statutes have changed very much.