Whilst it may seem like this is what would happen in a Zombie Apocalypse, what's going on in Coronavirus is much different. For one thing, there aren't hoards of people wandering around in a catatonic state (well, no more than usual, and quite probably fewer). It might be better if there were, because then we could see who has the virus and know who to avoid. Also, zombies have to bite you. You don't get infected by grabbing a handrail that's been touched by one; but this is a virus transfer mechanism.
We know that SARS-Cov-2, the virus that leads to Covid19, can live on some surfaces, like plastic and metal, for days. That makes it really difficult to avoid. How do you know who last handled the packet of lettuce that you've just spent an hour in a socially responsible queue waiting to buy? What about that shopping bag that's been left on your doorstep by the delivery driver? Or its contents?
On balance, zombies might be preferable to the silent, unseeable, virus that's causing the current pandemic.