"Pay less if it's not urgent" doesn't sound evil or anything. Like the pandemic has proved that delivery workers are a scarce resource, what do you want them to do, have a raffle?
In a competitive market, it really will be "pay less if it's not urgent". In particular, if you're a peon flying coach, you want some people flying first class, because they are effectively subsidizing your ticket. Bring on the rich!
The ecconmics of airplanes is different and do not apply. Here you want enough people paying for the cheap service that it makes money so they don't kill it. There is no advantage to a class of service that doesn't pay for itself in this space, you just move up to the next one.
Actually the worst thing would be most people choosing this as they may decide that the cheaper class isn't worth serving at all.
I don't think this analysis is correct. No one's going to offer a service if it's cheaper not to, yes. But if there's only one class of service, you have to make $X on each order to cover your fixed costs. If there are multiple classes, the cheapest class could end up being $(0.8X) and still allow you to make more money overall.
Think of it as an SLA. People optimise for different outcomes, some people need their groceries in a 1 hour timeslot because they have other commitments.
There's three broad ways to determine distribution of scarce goods. You've missed one.
In no particular order, those ways are:
1. Highest bidder.
2. Lottery.
3. Highest need.
There is no intrinsic 'fairness' to either of those three priorities to distribution - what any person thinks is the fairest method completely depends on their value system.
However, regardless of your value system, and your opinion on which of these is the most fair, you can probably agree that for luxury goods, #1 is a reasonably accurate proxy for #3... And that for life-necessary staples, it is not.
In the case of grocery delivery in the middle of a pandemic, people with pre-existing conditions, the elderly, and people living adjacent to those first two groups rank much higher on #3, than your run-of-the-mill 20-something-year-old. For the former, delivery is not a luxury good. For the latter, it is.
If they are truly life-necessary. But it is quite likely that the elderly and the pre-existing conditions folk will survive getting the bread tomorrow instead of in two hours.
We already have a bypass mechanisms for the "I'll die if I don't get it in two hours". It's the emergency services system and it's there when your life is in danger and it's currently overprovisioned to ensure capacity.
Which is why I was talking about grocery delivery as a whole, as opposed to two-hour grocery delivery.
The problem is if the express versus economy stratification does not actually increase overall system throughput - but instead, attracts more load to the system, as people who don't need it, but were otherwise going to the store end up using it for convenience.