I bike to Costco and Ikea all the time, but sure you do have to get big stuff delivered unless you have a trailer (https://www.bikesatwork.com/blog/move-it-by-bike-moving-serv...). I used to commute to downtown from the suburbs daily. When I was young my dad used to bike me to daycare/school all the time. If you need to be somewhere in a suit you bike in pants + undershirt and add the rest when you get there.
All of these things are possible, admittedly there is a real limitation of needing to live within a 15-20 mile radius of work. The best data I can find suggests about 23% of commuters have a commute of more than 20 miles. So I would say cycling is a perfectly reasonable solution for the majority of people.