The difference in selection is very real. If you need to buy one of those once in a lifetime things, you’ll probably find those in Amazon. The local stores have no incentive to keep those in stock, because they will probably only sell less than ten of those things within the next 20 years.
However, when it comes to phone chargers, towels, garbage bags or soap, my local store is perfectly fine by me. I don’t even know how much cheaper those things would be on Amazon, but I prefer to keep the local stores around. If I happen to need a very specific kind of charger with some special features, I’ll just see if there’s an online store for that sort of stuff. Usually there is and it’s also within a 1000 km radius of where I live. Sure, shipping usually takes a few days, but I’m in no hurry.
I guess the convenience really depends on where you live. In my case, it’s really simple to do most of my shopping as a part of my daily commute. The place where I switch between a train and a bus, there’s also a shopping center right next to the station, so why not.