I'm not a programmer. I believe it is possible to spam the mempool if nodes would keep the entire mempool. A single person can generate 1M transactions by burning 0.5 BTC. The mempool would be unable to store all of the valid transactions due to RAM usage. I suppose some nodes might keep some mempool transactions while keeping others on different nodes.
This type of spam like any other type of spam requires paying a lot of fee in total specially since it also increases the fee so for example if they start at 1 sat/vb they will increase it to 100 sat/vb while their older transactions with low fee would be dropped out of mempool.
With 0.5
BTC you can only create about roughly 100k transactions not a million.
Assuming average tx size is 200vb, then that would take up 20MB of a mempool.
You'd have to burn around 7.5
BTC to fully exhaust everyone's mempool.
Anyway, the fact that it costs 5 digits to pull off a successful mempool spam attack for no material gain shows how strong Bitcoin (and the Bitcoin price in particular) has become.