One of the big things for the no bag thing to work is planning and prep.
I always have a suit, 4 shirts and 4 sets of undies in the office. I have a small bag of shower stuff that also lives there. These both get replenished on my train days.
I also make sure I bring a week of food in on a Monday, again, it’s a habit and it happens every Monday.
I check the weather the night before when getting kit ready, if it’s likely to rain I take a small waterproof in a jersey pocket, if it’s getting cold then I pack arm and/or knee warmers the same way. Having compact, mostly roadie based kit really helps this. Today for instance I’m likely to get drenched coming home, hence having a waterproof gillet and arm warmers. If the weather changes during the day, well, I guess I’m getting wet/cold.
My wife also knows things need to be planned during the week in advance, in an emergency I can get the train home though it’s not much quicker, but it happens twice or 3 times a year
I know this level of organisation doesn’t work for all families, it didn’t for mine for a while, but with practise it works really, really well. I do accept the fact I have a rather long commute does strengthen by anti-bag bias, if I was doing 5 miles I’d be less strenuous in my arguments but still, do it if you can.