Are all parrot owners retired people or stay-at-home? No, they are not. There are parrots that live under the 12 hours of light and 12 hours of darkness we started following (as a great new 'discovery')back in the 80's as well as birds that live under a human light schedule. it depends on the species whether this works out or not for the birds and their owners. But it's very, very rare that it works out in the long run and, in truth, this is the reason why sooooo many parrots are rehomed. Because, as they get older, even the non-hormonal species (some of them are more 'hormonal' than others) start 'acting up'. People will tell you that they work full time and their bird is fine but it all depends on the definition of fine and the bird's age.
Can you keep your bird working full time? Yes, you can but you would have to make significant adjustments to what you thought you were going to have with this bird. For example, you could get a person to come in every day and spend hours with the bird so although the bird is kept at a solar schedule (which would prevent your interacting with it when you are home), she/he could have the necessary hours of flight and one-on-one with somebody (I knew somebody who had an eclectus pair that had a housekeeper that was there for the birds during the day but it could be a relative or a neighbor, too). You could find a birdy daycare and bring it there in the am and pick it up in the pm, covering his carrier so it's not exposed to light while traveling (I knew a dog groomer in Pa that had a birdroom in her store for this use alone). You could get the bird DNA'd and get him or her a mate so it's not alone during the day and still be kept at a solar schedule. Personally, I think this is the best solution because you could feed and clean the cage (it would have to be a flight cage, of course) in the dark (this is not that hard, I used to do it when I worked full time), put the lights on timers (real easy to do) and the bird would not bond to another human. Like I said before, when GCCs are kept in tune with the seasons and fed right, they remain affectionate to the humans even when they have a mate of their own and, besides, you would be there every weekend and, during the long days of the summer, you will be able to interact both in the morning and the evening with the bird during the week, too (I get up before 5 am during the summer so as to be there for the birds at dawn). Personally, I try to get mates for all my birds even though I am here for them all day long, day after day, month after month. I prefer it that way because, if I can get them to bond to each other, it eases my 'load' when it comes to their happiness. I took in a lovebird from a couple that had found it in their balcony and, as soon as I had switched it to a good diet and gotten used to me, I got it a mate and it worked out great! They love each other to pieces and Peachy still loves me and comes out every day to fly around and perch on my shoulder and give me kisses.
It's not impossible, it's just a bit harder and a lot different than what most people expect... But then, having a parrot is always a lot different than what we expected