I haven't been out to the grocery store myself, since I'm taking care of my two elderly parents (so I put myself in the "elderly" category for now to protect them), but I can say that delivery has been spotty but reasonable - we missed out on chicken and rice in our delivery last week, and lettuce this week, but we certainly have enough stuff overall. I went out twice to bulk up on supplies in early March, before the mania (and the COVID itself) hit, but it's always nice to have fresh food around.
I think also a lot of it has to do with people only shopping once every 7-14 days instead of shopping for the next 2-3 days - that's a smart move, as it decreases the number of exposures you have. It also has to do with people holing up and not doing any kind of delivery/takeout, or doing it less frequently - that will naturally increase the number of people shopping at grocery stores. (Plus, it's theoretically cheaper - if you're laid off from COVID and have nothing to do all day, may as well cook your dinner for $5 rather than get $10 of takeout.)
I like the idea of senior hours in the grocery stores, but I worry a little that it inadvertently gives seniors a false sense of security when shopping. If you're elderly and you've got kids or younger neighbors who are begging to shop for you - please, let them do it! Not a time for pride or being independent. But the early hours are a good second measure if that's not feasible.
And as far as the continued need, some of it is just people who haven't been able to get it in the first wave of panic buying. If you weren't able to get TP when you went out last week, you're still going to need it this week.