Earlier quoted context omitted.
It's not. There are a ton of comments about people reminiscing about doing exactly that. The problem is the corner shop no longer exists. And if it does, it's a chain, and the rotating staff won't recognize the toddler as being yours. Or going there will get your kid run over by an SUV. Mainly the latter.
I checked with my kid and shops no longer let little kids by cigarettes or beer. How customer unfriendly!
My mom asked me to pick up prescriptions at the local pharmacy starting I was 6-7 (we lived a few blocks away). The pharmacists gave them to me because she knew me and my parents. Blanket laws are easy to enforce, but they remove precisely this individual agency.