I do not see much of a difference between something being affordable in theory, but unavailable in practice, and unaffordable but available.

The latter offers some advantages:

1. Increased prices on scarce goods discourage frivolous consumption.

2. Vulnerable people, if they can be identified, can be subsidized or have their fees waived.

3. Those that find they really need a delivery can still book it - something that is currently impossible.

4. Funds can be raised for good causes.

5. People do not have to waste time queuing/trying to get a slot.

If you like, you could operate both systems at the same time - allocate some slots on a first-come-first-served basis, and some slots on a market supply-and-demand basis.

And of course, delivery is not a necessity for many: a lot of those booking slots at the moment could just go to a shop and buy the groceries in person. A market system would discourage them booking delivery slots.