Every place the rules are made tighter the system becomes harder to implement correctly and harder to improve in a backwards compatible way. One more thing which someone can be invisibly and nearly undetectably too lax on and cause a terribly hardfork if their implementation is ever widely used.

For example, I suggestion I'd made in the past is that someday transactions could contain small (32 bit) checkpoints against random blocks in the recent chain such that the transaction's fees can only be collected in blocks descending from that checkpoint.  This would allow users to make sure their fees are not funding a malicious miner who is mining a fork which is against their interest. Such a thing would require that the coinbase outputs be less than the allowed value in those cases.

Regardless, your invariant would also be violated by the duplicate coinbases or by unspendable OP_RETURN coins which should not be tracked in the UTXO.

This is by far not the most finicky or subtle implementation rule in the Bitcoin system.

Every time I see someone trying to reimplementing Bitcoin themselves my heart is crushed a little bit. There are so many things that need to be created in our ecosystem beyond yet another reimplementation, most of which are never completed, never made correct, and never widely used.