

Isn’t this what I just did?
mydomain.eu.cc
I mean the second part from the end (.eu.). That’s not yours, and that means that the mydomain. part can dissapear at any time. The owner can also do all kinds of unpleasant things that can affect your online presence.
By “your own” domain I mean getting something of your own in that 2nd spot instead of “eu”. It doesn’t have to be on the .cc registry, it can be any established TLD like .com, .net, .org, it can be a country TLD aka ccTLD like .cc, .nl, .de and so on, or it can be a so-called “novelty” domain like .dev.
Having your own domain means you can own it in perpetuity (well… old, established TLDs are better at this than novely TLDs) and have much better control over it.
Visit a domain registrar like Porkbun and have a look through their TLDs, check some prices, the privacy of your personal data etc.
Avoid registries that allow “premium” domains, it means that the registry can suddenly decide that the domain you own is very cool and force you to pay hundreds or thousands for the next renewal or lose it.
Wouldn’t connecting through an existing fedi server also enforce its blocklist down to me?
I’m not entirely sure on how you propose to use your server: if you just want to read stuff or also want to be able to post.
Your server can do things with another server in two ways, by exposing an open port and allowing the other server to do stuff locally through that port, or by connecting to a port opened on the other server and doing stuff there.
If the fediverse protocol mandates having a local port open to do stuff like posting, it may be impossible to avoid doing it.

I guess this can be useful when you can’t change DNS on the local router.
But wouldn’t announcing
*.local.domainfor the server that Traefik runs on accomplish the same?