I think it really depends on the city's density, but on the aggregate (at least in the U.S.) something like the approach you describe will win out.
There is a reason pizza has been the primary delivery food for such a long time-- most other meals are more complex to prepare/transport and harder to keep at proper serving temperature & texture. When you add customization to the mix, it's even worse.
Other foods are slightly harder to keep in good condition during delivery, but not so much that they’re not viable. Maybe it is a US thing, but here in a medium sized UK city I can see 29 different restaurants delivering pizza, curry (Indian and Thai), Chinese, kebab, and two different varieties of chicken available in just one of the delivery apps I have installed. I’m pretty confident that any one of them would be edible, and it’s current 11:30pm. During the early evening I can easily get a choice of ten or so cuisines from 40-50 restaurants across a couple of apps.
There is a reason pizza has been the primary delivery food for such a long time-- most other meals are more complex to prepare/transport and harder to keep at proper serving temperature & texture. When you add customization to the mix, it's even worse.