Current common belief is that on-chain fees must/will rise with adoption.
I don't think this will be true.
I think fees will stay relatively static in Bitcoin terms and will only rise in value terms.
I believe mempools will always clear.
Discussion
Interesting. I just wonder if the fees go up before a sidechain or altcoin comes in as the "silver" to Bitcoin's "gold" historically when transactions got too expensive another asset emerged. So either the fees go up nominally with usage demand or another coin becomes a secondary transactive unit and asset.