How does BCH secure the blockchain after 2140

BCH wants to make Bitcoin is scalable as possible, meaning that as many people as possible can transact on layer 1. BTC block space will be very scarce, but BCH block space will be abundant. My question is therefore -- how does BCH guarantee the security budget is high enough to secure the chain when the block reward is 0?

Justin Drake from Ethereum is making the argument that Bitcoin's issuance system is unsustainable in the long-term because it will rely on insanely high transaction fees for layer 1. It seems to me that this is an even bigger problem for BCH because block space is less scarce. Genuine inquiry, not trying to FUD.