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 Average fee per block is 0.0835 Bitcoin right now. That will be the same or higher in 20 years. The security budget is a solved problem which had been a part of Bitcoin since inception.

The block reward will be irrelevant by 2048. There are probably only 2 or 3 meaningful halvings left until the network is essentially in its end state. 
 I wish I had a plot of tx fees in bitcoin over time. Fees were 0 per block for years. But I feel like fees have fallen in bitcoin terms as price has increased over the years. 
 It's been volitile, but the number of transactions has been consistently growing. If it wasn't for segwit we would probably have higher fees than the reward already. We were on pace in 2016/17.

But either way, there is still no issue. Let's say hypothetically there are zero transactions waiting with a fee. There wouldn't be any mining! Which would mean no blocks. And after a long period of no blocks, eventually someone would want to use Bitcoin, so they would submit a fee and someone would mine it.

It's a pretty well contained, self correcting market. I could even see block time variance decreasing as transaction demand becomes higher and more consistent, and miners want to capitalize on fees. 
 enhancing the overall security of the network at a verified precision level