When you order an Uber, you are buying an included 2 minutes of wait time plus the option to pay by-the-minute for wait time thereafter. This is part of the contract. One way you can tell is that if they wait 90 seconds for you and then you cancel, you get a bill for ~$5.

Shared rides (Uber Pool) is different. In that case, you're making other riders wait and, unlike the driver, there's no reasonable way to compensate them for the time. Thus, being late is rude.

If one could reliably order an Uber that would be great. But no way Im waiting outside in -10C while the app lies about someone about to pick me up.

Somebody is going to wait for somebody. When you order the Uber, you don't know exactly when it will arrive, so if you don't want to make the driver wait, you have to go to the curb ahead of time and wait there. The implicit assumption is that the driver's time is more valuable than yours.

I would very much like to have an option for the driver to simply be fairly compensated for their waiting time so that if I want to leave at 12:00, I can order it at 11:45, and they'll just wait until I'm ready to go. Higher end traditional car services will often show up half an hour or more before the scheduled time so that they can be absolutely sure to be ready when their customer wants to go. It would be nice to be able to get this level of service from Uber (for a fair price) without the driver being upset about waiting.

It should be an option to pay for them to wait in a way that’s fair to the driver. There are valid reasons for a few minutes wait. For example, getting picked up from a train station in bad weather.

Maybe i'm in an a/b pool, but uber charges me if I make them wait longer than 2 minutes.

So yes, they are being paid. And even so, it wouldn't be so much of a concern if uber just paid drivers fairly.

1mn-2mn wait is rude? What world do you live in?