It just doesn't solve any pain points for me, I don't think.
Maybe one. The only pain point it possibly might solve for me is the the advertised price is not often the real price. (For example, an $8.99 pizza is only $8.99 not counting delivery fee, tip, and the fact that to get it at $8.99 you must order two. This is often obscured in ads and such for obvious reasons)
That's maybe the only pain point I think it could solve. The rest of the modern delivery process is just that, pretty modern for me. I can't recall the last time I ordered pizza not from a computer that remembered my address, preferences, etc. I've never used an app, but I bet if I Google there are a few I could choose from.