Making up a bigger fraction doesn't mean that transaction fees will increase over time.
For L1 fees to actually increase over time, we need increased L1 throughput. Without that, increased demand for transactions causes more batching of transactions (mostly between exchanges).
Given the failure of BCH for pseudo-religious reasons I don't have much hope.
To clarify, I don't see users ever leaving centralised exchanges.
That means classic claims like "bitcoin is scarce" or "transactions don't require anyone's permission" or "transactions can't be censored" or "nobody can seize your bitcoin" are generally false in practice.
Even if a person only trades via bags of cash in dark alleyways and never touches exchanges, they're affected by all this "paper" bitcoin.
If they need to touch an exchange at any point, even if holding in a cold wallet 99% of the time, that exchange can still take 100% of their tokens.