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