Unlike on-chain transactions, off-chain transactions aren't limited in capacity, so market mechanisms should lead to an equilibrium between cost and profit. If fees go up a lot, new parties can join the LN-routing-market and fees will go down again until there's a new equilibrium.
Isn't that the same as mining, hashing power, and demand? Because offchain channels are also as limited as the amount of capital, the Bitcoins held, the users have.
No amount of hashing power, capital or earnings per block can increase the number of transactions Bitcoin can process (I'm ignoring small fluctuations until the next difficulty adjustment).
With LN, anyone with some coins can set up a node, which increases the number of available routes. The new node will need to connect to some nodes (or users). I've seen
several offers from node-owners that pay to open a channel with them.
I was talking more about on-chain, limited block space, if higher tx demand = higher fees. Off-chain, limited capital available, therefore limited payment channels, if higher tx demand = higher fees.