It makes sense. Just like "economy" vs "first class" for travel. As a business, it needs to partition out the consumer buckets into various groups for profit maximization.
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.
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.
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.
Actually the worst thing would be most people choosing this as they may decide that the cheaper class isn't worth serving at all.
As a thought experiment, suppose there are a few local zillionaires start making "platinum" orders to local markets each day, with a $1M delivery charge. Will the markets stop accepting otherwise-profitable peon orders? No. That part is easy. But what will happen to the price of peon orders as the markets compete? They can afford to lower those prices a bit, since their fixed costs are spread across all customers, and the zillionaires are already paying the lion's share.
If you doubt this, imagine you run one of the markets and your competitor drops the price of his peon orders by five percent. Are you going to allow the competitor to take all of your business, forgoing the profit you'd otherwise earn?
When you're stuck with an empty cardboard roll in the middle of a three-flusher, you'll pay whatever price Wal-Mart asks.