Will spam make the Bitcoin system sick, like a tumor? Just like many people are willing to spend a lot of money to eat junk food, and finally lead to a higher probability of cancer in the body. Nothing bad, just a worry. π
Discussion
When spam becomes uneconomical spam stops. Higher fees for longer will solve that. Just giving money to good economic actors.
When what you call spam becomes uneconomically, that will mean fees are higher than they are currently. Which means less people will be able to afford onchain transactions.
Fees go exponentially down over time as issuance goes down over time. The first fees were like 1btc to move anything. The reality is 95% of people will never control a utxo. They will have shared custody of a utxo or straight non custodial btc.
Spammers need to pay like everyone else. Bitcoin doesn't use white blood cells, or any cells, so it'll be fine.

