I have shopped online since the service was available (the 90's?) and it is maddening that it has become so difficult to get slots now that people who didn't want them before have changed their minds, particularly when some people have been booking up slots for weeks ahead.
Sainsburys seem to me to have the right balance. They deal with the vulnerable first, then release slots to pass holders, then after that open them to everyone else. You get an email when you can book a slot, and they only allow one per week, with restrictions on the number of items allowed.
It's impossible to be really fair to everyone, but I think that is as good a system as any. I feel sorry for people buying for families, though, as they are still restricted to a maximum of three of any one item. I don't know how that works if you have a family of four (or more), but I understand that they have to stop idiots from buying up all the loo roll.