I want to believe that this ordinals plague can be stopped before it grows to gargantuan size.
I'm afraid that the only manner to slow down the damage of this nonsense is to rise the block size limit.
Or perhaps increase fee for NFT transactions?
Impossible without hard fork. Currently fee rate is only based on transaction size.
I'd say impossible-- period. You can't arbitrarily force on a protocol level what you find appropriate fee. That's a miner's job. And if we reach the phase where we don't treat each byte equally, we're censoring.