How would this affect miner profitability, and thereby security, long-term, if as you say on-chain would be dead, long term? The BTC value would have to rise quite a bit over the coming century for it to be profitable to have even today's levels of mining on one or a few UTXOs from this system, with block subsidies going towards and eventually to zero.

Not saying it's unsolvable, guaranteed to be a problem, or anything, just wondering.