This would be really useful. I've had 2 people so far sign up to my new site who have been put into moderation. Both of them a people I personally know, and ar registered on my other XF site, so it would have been good to see exactly what triggered the moderation.
From what I can see in the ACP, it doesn't log anything. I had a spammer try to sign up on my dev site as it's not behind a .htaccess at the minute while I test some things out, and the option set is manually approve when at least 1 of the warning flags are triggered. There was no log of this sign up, and as I rejected it, that doesn't appear to be logged any where either.
I would love to see this. Various addons also send accoutns to moderation. It would be nice to see if an account is moderated because of a blacklist, because an addon sent an existing account to moderation for some reason or something else.
XF 1.2 introduced spam management tools that could cause content to be moderated or blocked entirely. Unfortunately, it was sometimes unclear how frequently these options were being triggered. Similarly, in some cases, it wasn't immediately obvious why the options were triggered.
XF 1.3 adds the spam trigger log to help resolve this. This has several parts:
A general log view in the control panel. This allows you to get an overview of each time content (or a registration) has tripped the spam tools and why, along with full information in the request to help determine if it was tripped correctly.
When viewing the list of users awaiting approval, if they were put there from an anti-spam option, this will now be displayed with additional information (if available).
So this includes Stop Forum Spam, users who share IPs with banned members, etc. By default the only thing that doesn't show as a reason for a user being moderated is if they've been moderated manually or moderated as a result of the option to moderate all user registrations.
It has never been impossible for add-on developers to add information there. They could either populate an entry in the spam log (if it's a spam related reason) or create their own log for it.
In XF2 we also introduced displaying the "Change log" for a moderated user. This is useful as it will display cases where a newly registered user has modified certain profile fields (including custom fields) which may contain spam content.
So, going to call this implemented now (though mostly has been for 4 years)!