This is the chart of Bitcoin's Avg. Transaction fee:
https://bitinfocharts.com/comparison/bitcoin-transactionfees.htmlRight now the median fee is about $2. After lots of halvings the reward won't be enough to satisfy the miners. I guess that after a decade, bitcoin will be more widespread, as a result, more transactions will occur every second. Won't this increase the median fee? If it does, bitcoin will start being a not-so medium of exchange. Imagine paying $5 for a transaction. Even paypal doesn't charge that much.
When price go up enough so that the fee is problematic, well, price has gone up, so in general people transact less amounts, less bytes per transaction = less perceived fees. Say we reach a point where 1 satoshi = 1 USD, a current transaction cost would be in the thousands of USD! But a regular transaction of around 1000 satoshis, costing some 2 or 3 satoshis wouldn't be too out of the ordinary.
The chain will evolve, some miners will move on, but this is my perception of how fees will stabilize in the future, adoption is going to grow so price will follow as well. (the above is NOT a price estimation, it's just an example)