Ocadao and Morrisons have delivered to us throughout the lockdown though in the case of Ocado they did at one point have a rule about delivering only to existing customers from before the lockdown but that has been relaxed as well.
Given the sheer scale of the lockdown and following disruption the existing supermarkets have handled it really well except for the toilet paper situation which was beyond silly on the consumers part and there really wasn't much that the supermarkets could have done at that point.
I'm in the UK and have had weekly Tesco deliveries consistently through this period. They do leave them at the gate now instead of carrying them in but other than that, and an 80 item per order limit, business as usual.
Tesco and ASDA have both been delivering to anyone throughout, and Sainsbury’s has opened out to anyone in the last week or so.
In the Uk Amazon had this policy too but in reality most non essential/but useful items were sent to me in less than a week.
Of course most of the very useful items were not in stock at all the first few weeks, and some still aren’t.
Edit: good lessons in not depending on one supply route and as a result I will buy my fresh food from smaller companies from now on.