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.
Exactly this is the main point.
While nobody will believe you that you've thrown away the private key for 1MocACiWLM8bYn8pCrYjy6uHq4U3CkxLaa, it's pretty much unlikely (heh 99.9999999%) that you or anyone can have the the private key of
1111111111111111111114oLvT2, 1BitcoinEaterAddressDontSendf59kuE or, why not, 1JasonBrendonHasMuchToLearnwzf2iV, simply because they are far too long to be vanity addresses.