No, working parents don't look after a child all day but they aren't in the home all day either.
They do the childcare when they are not working and still manage to do everything the OP puts as a priority.
Children or not, if I came home and my partner had cooked a meal and exercises while I was expected to clean, tidy and to do other odds and ends I'd be annoyed.
As myself and other posters have pointed out it takes minutes to pop a wash on, to tidy as you go, put dishes away and maintain a relatively clean house. No one has stated they expect a full spring clean every day.
If a poster came on and said "I am a working mother and my husband is a sahd. During the day he takes toddler to pre-school, makes dinner and exercises while expecting me to work and then come home to clean, tidy, look after the children etc. Aibu to ask him to do more?" The general consensus would probably be in the womans favour.
This isn't about who stays home, this is about the OP thinking cooking, childcare and exercising is the same as working, cleaning, tidying and childcare.
If you are a sahp then you take over the role of providing childcare and looking after the home during that period until the working parent comes home at which point both chip in. If you are both working then it both falls equally on you.