Papers really probably Ought to be changed daily. I admit, I do not always do this. At this point I am probably changing papers maybe every other day and even sometimes going to three days. My birds do have huge cages and do not choose to spend any time on their cage floors, regardless of papers. (Also, my conure prefers to avoid pooping in her cage, if she can convince me to come get her instead. She likes to poo on me or any other surface, preferably IN the bathroom if she can get me to take her there, and then likes to Yell at me until I wipe it up and discard the tissue. So her papers are often not too messy.) BUT really I Ought to be changing papers every day anyway. Changing the papers is Not a difficult chore!
As far as sanitizing the cages. I think it depends what you mean by that. At this point, myself I do Not remove my birds and scrub everything down with a solution weekly. I think that would be excessive. BUT. I do keep scrubber-scrapers nearby, I keep an eye on the cages, and I often just reach in and knock off any buildup. I do this anytime I notice buildups, and also daily before changing water / food / papers. (Wash my hands afterwards of course.)
Beyond that, I will also take a good quality Micro Fiber cloth with HOT water to clean the cages, their perches & toys, etc... I'm pretty random about this, but probably more than twice a month. The birds usually remove themselves from their cages while I do this, but they don't have to, as it is only water. (I find that microfiber and HOT water is usually all I need for most cleaning purposes. HOWEVER. There are no children in my house and I keep the hot water heater in the red, so my hot water is Steaming Hot from the tap. Normal hot-tap-water would probably Not be sufficient in most cases, and vinegar is a good choice for cleaning, as long as you rinse it well afterwards .)
As far as the food and water, this has to be changed daily, and the dishes -- especially the water dishes or any containers with non-dry food -- especially must be kept clean at all times.
OH! Also my birdies like their shows in the form of spray-shower IN their cages. They like to get totally soaked, which also thoroughly soaks the cages. Once they are finally done, I wipe down the cages with micro fiber cloth. AND when I do, I pay extra attention to any spots that seem to need cleaning. THIS might be the reason their cages rarely need "sanitizing", and also why I don't know how often I do it. Sunny demands showers randomly, some weeks almost daily, some weeks only once or twice. (The budgies don't usually request, they usually just wait till Sunny makes the demand.)
So basically if you keep cages Clean as you go along, you may not need a full "Sanitizing" every week. But if soaking and wiping down your cages does not happen frequently, then perhaps you should add to your calendar & make sure you do so often, and weekly would probably be a good idea.