The Uber Eats delivery time estimates are a lie, plain and simple. Once they have your money in hand, they'll shamelessly admit to the lie, which is why the estimate jumps instantaneously.
First, there are three different ways that orders can come in. 1) Tight integration into the POS system. 2) Through a separate parallel physical tablet. 3) Something spits out something on a printer.
There are opportunities with 1 and 2 to do some sort of feedback on how busy things are. I know for the tablet option that at least for some restaurants they are able to indicate how long the order will take.
But half the places I get to have no integration, they just put the ticket on the pile and it's done when it's done. A couple places that do this in particular also don't even start the order until the driver shows up, on purpose. The app will tell the customer I'll pick it up in 5 minutes no matter what. There's a chain that does prep work in front of the customer, but certain locations will not make pickup/delivery orders if there's anyone in line in the shop. I stopped doing deliveries there.
You'd also think that places with the potential for awesome metrics making pickup timing a breeze would be fast food chains, right? Nope. Not a single iota of smart integration whatsoever.
I've found that keeping customers in the loop as to what's happening with their deliveries ends up keeping them happy, even if it's gonna be slow. I suppose some things never change.
Talking to people really does help though, everyone wants to be more forgiving when you remind them theirs a human factor involved in getting the food to them.