I think Sainsbury’s are handling this well. I am a regular customer, and have so far managed to get a slot most weeks. After the vulnerable slots have gone, they then release them to regulars, which I think is fair.
They don’t let you book for weeks ahead, so there isn’t a situation where some have slots booked up for ages and others can’t get one at all, and new online shoppers can’t just ‘push in’ ahead of those who have used the service for years (and will, presumably, be their core online customers when things go back to normal). When the ‘regulars’ slots are used up, they are released to everyone else, if there are any left.
There is a number you can call if you are vulnerable, so you can go on the priority list (which is good), but after that they are showing loyalty to the people who have shown loyalty to them, which is rare these days.