I wouldn't know how to remain anonymous by running my own server. Unless I use a prepaid sim card for its internet. OK, that might work.

But in terms of deleting your records, there is no such right. If you run your own server, and I copy data from it, then you can burn your server if you want, but I will still have your data. There is no avoiding this. So with relays you might actually have better chances of deleting.