The only hand that Yelp has in the process is delivering a convenient form that passes your order to services the restaurants already work with like Seamless, Grubhub, etc. It's no different than if you had visited GrubHub, placed an order, and the restaurant got it to you late.
Sorry, but every additional middleman involved is another potential bottleneck or point of failure–even if it's as trivial as an embedded form or redirect.
This is exacerbated on mobile, which is the majority of Yelp's traffic, where connections are slow/spotty.
