Are there benefits to hosting your own personal lemmy?

Yes. I am immune from the beehaw/lemmy.world drama or similar. I can block instances as I please and I can tinker with my instance.

There is already drama? Lol
- Eh, kinda. lemmy doesn’t have super great moderation tools yet, and the influx of users on lemmy.world and lemmy.ml included people posting some content that was against beehaw’s moderation guidelines. Rather than deal with being overwhelmed without much option, they decided to temporarily defederate until there was a clear path to resolving the issue (i.e. better mod tools).
  I think people are making it out to be a bigger deal than it really is, and those flames are probably being stoked by the trolls.
  There are plenty of “no actually assault weapons are good for society” and “actually Ukraine is the aggressor” groypers around now, but I guess that just means Lemmy is getting popular enough to attract the masses - which in the end is a net positive.
I can tinker with my instance.
I didn't even find a SANE way to set it up with Docker without having to tinker with the instance. I just want a container not generating half a dozen of other containers and volumes.
- A single container for everything gets away from the point of containerization. If you have a single container for lemmy-ui, lemmy backend, and postgres, you need to rebuild that container whenever any one of those applications gets an update, and they could start to interfere with each other. Keeping them in separate containers makes everything a lot cleaner, it just requires something like docker compose to put it all together.
  Did you try the Ansible install? Provided you're installing onto a supported Debian/Ubuntu version, I found it fairly straightforward.

There are two big benefits in my opinion.

Speed and responsiveness. When the bigger instances were (or are) overloaded, my Lemmy experience was still fast and snappy. Content was slower to update for those big instances, but navigating Lemmy itself was still fine, and it gave me an opportunity to engage with some smaller communities.
Control of federation. I decide who to federate with, and as long as I follow other instance and community rules, I won't get defederated.

The biggest downside is that I can't discover new communities organically since I'm the only real active user of my instance. Nothing new gets federated unless I seek it out. But I solve that by using a fediverse indexer every week or so to search for popular or interesting communities.

But I solve that by using a fediverse indexer every week or so to search for popular or interesting communities.
Is there a way to automatically federate with other instances? Because I started my own Lemmy instance, and its annoying having to manually go to every community in order to federate with it. (The instance is for my own personal use, so I won't be opening registrations)
- Absolutely, there are two tools I use to do so.
  Lemmy Community Seeder - Very customizable tool that by default grabs the top 50 posts in the top 50 communities of the specified instances every few hours.
  Lemmony - Less customizable tool that by default grabs pretty much everything. Probably less ideal for larger or more active instances, but my instance has 5 or 6 users, only a couple of which are active, so this tool has been awesome for populating my "All" feed.
  I recommend creating a non-admin bot account and using that for these tools.

You end up as the ultimate decider on what you federate with. If you join someone else’s community you might not agree with their administration or moderation decisions.

It’s a fun exercise in system administration, it taught me some new things. It got me interested in Rust as a programming language (not that you need to know that to run an instance - I was just tinkering w: source code)

More private, if you're overly conscious about your IP being tracker by instance host
You own your data
You can experiment with alpha releases
You can customize everything. Default CSS, javascript, etc
You can't be censored (only defederated)

Not the OP, but can you move your account to a private instance or is it not possible at the moment?
- It's not possible at the moment. Lemmy devs acknowledged it was a widely requested feature but last I read, they were focused on maintaining the performance of Lemmy during the spike of users during the great Reddit migration.
- Not yet, that's (open) issue #1985: Moving user profile to a new instance.
  The devs also explicitly mentioned this request in their statement:
  we are seeing lots of requests to implement major new features, such as migration between instances, or combining similar communities. As described above, we are completely overloaded with work, and definitely won’t have time to implement these in the near future. If there is a feature you want to see implemented, you will likely need to work on it yourself, or find someone who can.
  For now, you can create another account on another instance and use that instead (or both), or just peek how the experience might be.