You can easily zap on chain, or even on a side chain such a liquid. Or better yet, we can run our own side chain with elements. On top of that payments can be batched, by reliable relays and only cashed out after batching, making on-chain fees tiny. The batching itself could use taproot and schnorr which would be native to nostr, and have tons of innovation adjacent such as silent payments. This is also lightning compatible.

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Funnily enough, on chain zaps would be far better than LN zaps, just not economically viable for dust zaps
I think few realize how cheap side chains can be. And that anyone can run one. You just need a 2/3rd majority of nodes that will not cheat. Now that we have a few reliable relays, they could bootstrap a new economy, then add more with dynafed, that the users trust. The cost of storing transactions would be insanely low, and therefore, so could the cost of on-chain zaps. You can also add things like silent payments and confidential transactions for users that want privacy with a slightly bigger tx. Plus enable op codes and all sorts of new innovation, as liquid has done. Fees could be a fraction of a sat, competing with lightning. But lightning could also be used. And dont forget that lightning can live on top of a side chain. Taproot opens up so many possibilities we have yet to explore!