But most of the moderation is done by community moderators, not admin. So it isn't necessarily the face of the instance but the face of each individual community.

However, if the moderator doesn't assign their username to the moderation action, then you can't really tell who's done it. It just says "mod", but it could be a community moderator, or it could be an admin. I can understand a mod not wanting to publish their username with the action, but it should still at least tell you what capacity they were acting under. Generally, I think instance admin are more sensible (with the exception of hexbear).

Also, when you load the instance modlog you'll end up seeing moderation from every other instance, and it doesn't even tell you which community it refers to most of the time.

Well, I've never come across anything that made me notice, which is certainly a good thing.

As of a few months ago, lemmygrad is run by them as well. I don't remember the specifics, but there was talk of some form of taking over every other Lemmy instance as well (I know there were calls for it from at least one of the tankie communities, either lemmygrad or hexbear), and the general hostility of both lemmygrad and hexbear users was why many instances defederated from them at that time.