On the Script page of the Bitcoin Wiki, in the "Provably Unspendable/Prunable Outputs" section, it gives an example of a script which would make that output of the transaction unspendable. In the example they give,
The unspendable output has zero value so the entire input amount goes to the miner of the block.
But if that output had been given some value of bitcoin, would I be correct in assuming those bitcoins would be provably unspendable forever? If that is the case, what is the need of a black hole address like the bitcoin eater? Couldn't bitcoins be provably "destroyed" simply using such an unspendable script transaction output?