Nor do I, but the fact that the system makes the miners have a less incentive over time, scares me. There will be times in the future where a miner will earn less than 0.001 BTC for solving a block including the fees. If we assume that the supply (of both $ and BTC) remained the same and compare with the current security, one bitcoin has to cost around 231 million dollars. (~7*33000 = 0.001*x)
Miners do not earn 0.001BTC per block for the fees, that is absolutely absurd and should never happen. Currently, miners earn anywhere from 0.1BTC to 1 BTC depending from the network conditions. Average count for the transactions appears to be about 2000 per block, so that is far lower than any realistic estimate for any mass adoption, with LN or not. If we were to make optimizations throughout the years and/or make the block size larger, then I don't see a problem with fitting 10x that in a hundred years, maybe even lesser.
Currently, network throughput for the miners is about ~100EH/s, at it's peak was about 170EH/s. That is quite a large number and shows that even with current block rewards, it is very very far from being remotely profitable for any attackers. Remember, you don't only pay for electricity, you also pay for the ASICs themselves, the landspace, etc. I don't think it's too far of a stretch to assume that by the time block rewards are <1BTC, the fees wouldn't supersede it. It should only be a concern if the network becomes insecure *enough* to be attacked, not if the cost of mining can't be matched with the current estimates.