--snip--
I do have the doubt though of how one can distinguish a vanity address from a burn address, whereby the former will be in control of somebody as (theoretically) opposed to the latter (perhaps the length of the legible part of the public address is part of the answer, but it seems like a simple non-exhaustive criteria).
AFAIK, there is no 100% certain way of telling which is a burn address and which is a vanity address...
This being said, it would take gazillions of years to create a vanity adress depicted above, the odds of finding an address like that within a lifetime are so close to zero that you can safely say it IS zero.
If you see an address like my vanity address: 1
MocACiWLM8bYn8pCrYjy6uHq4U3CkxLaa you can easily see the "vanity" part is only 6 characters... If you have a GPU farm and a lot of time, you could probably go to 10 or 11 (i guess, not calculated tough), but more than that doesn't seem feasible.
A second thing you can look for is a block explorer: if an address looking like a burn address was funded with hundreds of BTC over many years, and not a single unspent output was ever spent, odds are big it's a burn address...
Last but not least: any address can be a burn address. If you generate an address without a private key, or you immediately destroy the private key after generation, it's a burn address... But it's kind of hard to prove a "normal" looking address is a burn address... Anybody could generate an address and just say it's a burn address.