this would reduce the size of the mempools, and make it easier to run a node, and save space on the blockchain. It could be done like a difficulty adjustment where the minimum fee increases if the average block is >90% full, and decreases otherwise.
You are supposing there are a lot of people spamming useless transactions of 1 sat/byte? Transactions which would not be made if the fee were 3 sat/byte?
I don't think so.
You are basically penalizing honest users, like me, who like to do 1 sat/byte transactions. Whoever is attacking the network would attack at 3 sat/byte as well.
I don't think this would have the impact that you imagined, and this kind of interventions in the fee market will probably do more harm than good in long term. There is a delicate balance between fees, transactions, miners, etc.