IMHO the minimal fees will be 1sat per transaction, i.e. the small TXs will need to "overpay" to get to 1 final fee when the -minrelaytxfee is the minimum — 0.00000001.

But everyone will know that a TX with minimal fee will not live in the mempool for long and will never get mined. That's a real market. When the mempool is full all the time and minimal fees are minimal (not like the current default of 1000 sat perkvB).

But that's just my opinion after thinking about it and running nodes and explorers for years.