>To date all major tokens have either a fixed amount of tokens right away or eventually (e.g., BTC) or a rate of inflation that asymptotically goes to zero (e.g., ETH).

These are both incorrect. BTC has inflation that asymptotically goes to zero. ETH has undefined inflation (the current codebase has constant inflation, but has a "difficulty bomb" that is supposed to force a hard fork that will presumably change the inflation).

EDIT: I think I read the OP incorrectly, I think what they meant was that while the rate of coin issuance in ETH is fixed, the inflation as a % goes to zero, and that due to quantization BTC issuance actually hits zero.