I wouldn't put everything on LN -- it's a different protocol with a different security model. You need to keep private keys online. Its usability can't compete with Bitcoin. Etc.
I also don't think there's evidence that high fees reduce demand for Bitcoin. If anything, there is a correlation between rising fees and rising price. I don't buy the argument that $10-$20 fees matter. In fact, I believe on-chain fees will be much higher than that in the future.
I see higher fees as a good thing, not a bad thing. In the future, there will be no block subsidy. If users won't pay what Bitcoin's security costs, there is little incentive for miners to honestly secure the blockchain. This need is much more important than the need for users to have cheap fees.
LN is the most important development that will complement Bitcoin in order to have it function as a currency, which as time goes by, becomes more expensive on-chain as the reward dependence on fees picks up pace.
LN is one of many possible complements. Altcoins, sidechains, and other offchain protocols/methods can offer other alternatives. The point is that the fee market is well equipped to deal with this problem. Too much demand per block = fees rise too high = users/services pushed to economize their transactions, use other protocols, etc. Then fees drop, although we should expect them to trend upwards over time given limited block space and growing demand. I just see no reason why we wouldn't see $10-$20 fees in the future. It's going to happen eventually. And we'll have plenty of options to avoid them too, for day-to-day transactions. If you don't
need Bitcoin's level of security, other options are likely fine. The same goes for Lightning: It can't provide the same security guarantees that Bitcoin can.
Who are the users that are going to pay for the lack of block rewards? It won't be the mass, because they won't be bothering with Bitcoin anymore if there isn't anything else to use, which is why LN is so important.
Then perhaps price should fall, miners shut down and difficulty adjusts downwards. Less users, less fees, less security. It's all already built into the design.
People right now 'don't mind' spending $10-$20 on fees because there is a speculative incentive that makes it worthwhile to cough up these fees. What incentive is there when there is no severe volatility and upwards potential left anymore?
Security via honest mining. That was the design.
