My closest friends have two young children, and a 2/3 acre plot in which their house sits. They both have jobs. They are pretty much self sufficient in vegetables including potatoes and onions. They did say they usually buy seedlings in rather than grow from seeds, except for things like carrots where you have to plant seed, as they do not have the time to faff around looking after delicate seedlings.
I grow vegetables in my modest garden and have been self sufficient in most apart from rice and potatoes, for many months now, with minimal effort. If you only have to walk into your garden, you can spend half an hour pottering about and achieve a lot. I was busiest in March and April. To be fair I did have to do a lot of work to prepare the beds (serious digging to remove perennials and fill two disused septic tanks with flints, then completely re-landscape the lawn. But if you care about it looking smart, I’m sure you can just pile on compost, and wait for it to sink in. But once that was all done, there was not much to do. Spreading compost takes one weekend. Planting seeds takes a few hours. They need a bit of watering till they sprout. Raising module plants does take a bit more effort. It’s also working out cheaper than shop bought veg, which surprised me, and the quality is far superior.
I think the problem with an allotment is that you have to drive/walk to the place, and back, which takes maybe an hour of your time, along with transporting stuff, or locking it away in a shed, then clearing weeds cos many are endemic on allotments as are pests. I grew carrots last year without nets and got no carrot fly. And you might have to do huge amounts of work to prepare it for use. and you perhaps can’t leave out anything expensive cos it might get nicked.