At some point in 2011/12 miners started using custom mining algorithms ignoring the best practise to mine to a different new public key (hash) for each subsequent block. This lead to a lack of uniqueness of the coinbase transaction id and destroyed some bitcoins forever.

So it became mandatory with BIP34/v2 blocks to put the height of a block in a special encoded format into the coinbase transaction's input "script".

But why not use existing datastructures like the coinbase transaction's very own locktime field?