There are ways to provably burn coins, by sending them to outputs which have invalid scripts and so can never be unlocked. We can say with 100% certainty that such coins will never be spent, because there is no way to unlock them. Coins sent to burn addresses are different - there is a way to unlock them, it's just that we assume nobody knows what it is.
This right here is a fantastic security assumption when burning bitcoins.
If we really want people to be CONVINCED of the coins being burned IMMEDIATELY (not after the coins weren't moved for 20 years) then we need to burn them with a OP_CODE that makes the coins verifiably non-spendable.
Using the likeliness of the private-key not being recovered from the public key is really not enough as people can easily fool people by using keys which merely look like burn addresses. Users wont verify them and will end up sending money to a scam. If coins are consensus level non-spendable there would be no chance of this.