It's impossible to predict right now because no one knows how much bitcoin will be worth, how many people the network will be able to support in future and what percentage of the fees paid by those users will go to miners if off-chain services become a thing. It's all pure speculation at this point.
How would Bitcoin price matter when we are talking about fees? The Bitcoin price wouldn't make any difference, only if Bitcoins are being mined.
That part depends on whether or not fiat crumbles or if people still want to think of Bitcoin as an asset that they can exchange for cash. The more valuable bitcoin is, the less miners will need to cover their operating costs. If people aren't including enough fee with their transactions to make things profitable for the miners, the miners can elect not to include those transactions.
But to further complicate things, this also depends on how many individuals as opposed to how many large companies are using the main chain. Some envision that the average person in future won't be settling on the main blockchain, as that will generally be reserved for the finance sector and big business, who would naturally pay large amounts in fees. I'm not sure this is a likely outcome, though. I don't think we'll ever win the finance sector around to a system they have no control over.
Any variation in how the ecosystem develops over time, including things I haven't even thought of, could all have an impact on what the average fee might end up being in future. It's pure guesswork and anyone who says different is lying.
