> Yes because it’s completely safe to bike everywhere and how would I bring the groceries back?

Pannier bags. I did this for years. Before I got panniers I filled a big camping rucksack and cycled, but I wouldn't recommend that. Use a small backpack in addition to panniers if you have to, but having just the panniers feels the best.

However, in terms of safety you are unfortunately right. I didn't have a car so I went everywhere by bike but I was essentially a third class citizen in many places. Felt like I could just get wiped out and nobody would even care. There were no people around, only cars. I hate cars, so I had to get a car too :(