This is exactly how replace by fee works. If you use the same inputs, only one of the transactions can be included. The reason it's called replace by fee is tha

This is exactly how replace by fee works. If you use the same inputs, only one of the transactions can be included. The reason it's called replace by fee is that unlike Satoshi's original design for transaction replacement, which he disabled because it could be abused to waste node resources for free by repeatedly replacing transactions, it requires a higher fee for each replacement to discourage abuse. (Bitcoin Cash subsequently removed replace by fee out of some weird belief it was an attack on Satoshi's vision; this was of course nonsense, since he specifically designed transactions to be replaceable. It was also pointless, since it's a voluntary miner policy rather than a consensus rule and there's economic incentive for them to support it.)