never thought of this good idea, so after all the car is not necessary even for grocery, but I guess parking would be issue unless you live in house, not that big deal to find place for ebike/escooter or leave car on street, but trailer inside?
Lots of apartment buildings have street level storage usable for bikes and trailers, eg in gated inner courtyards or dedicated bike storage rooms. But trailers are not very attractive vtargets for theft anyway because they are cheap and there aren't that many trailer users.
not where I live, people here park bikes either in their apartment or in their cellar, which is usually very small, parking it in some common area on building would be quite rude towards other residents blocking the space and nobody will dare to park bike on street overnight