How frequently the cage needs to be cleaned absolutely depends on cage size and bedding depth, and I don't think you'll find anyone who disagrees with you. Bedding depth in particular is a huge deciding factor - you could have a 1,000 square inch cage, but if it only has 2cm of substrate (for example), frequent cleanings are a must. This is why it is stressed that hamsters have large cages (at least 80cm x 50cm for dwarf hamsters, 100cm x 50cm for syrians as a bare minimum) with in excess of 6"/15cm of substrate and advise that instead of fully cleaning the enclosure, instead recommend to spot clean regularly and remove small sections of bedding every 4-6 weeks (for enclosures of bare minimum size; larger enclosures with deep bedding depths often don't need large bedding changes at all, and can often be maintained solely by spot cleaning alone) so that stress experienced during cleaning is kept as minimal as possible.
If the enclosure requires full cage cleans (and we are talking in the case of an average, healthy hamster - not a sick one, or one rearing their young, etc where exceptions are made) it is a sign of either an inappropriately sized enclosure or an inappropriately set up enclosure and these situations are addressed as required.
Some hamsters have particularly disgusting nesting habits, and for many the providence of a multi-chamber hide with dedicated corner toilets (that can easily be removed multiple times of week if needed to be, without disrupting the actual nest itself) removes these habits. In the off-chance that it doesn't (which isnt the norm, but like winning the lotto; it can happen), then exceptions are made to prevent health concerns such as urine scold from occurring. I do agree that situations do need to be assessed on a case-by-case basis, absolutely - because there are certainly exceptions to every rule and although hamsters are generally very clean animals, not all hamsters are clean haha.
I don't frequent this forum often, but when I was more active on hamster forums in the past, we would never discourage from regularly cleaning sand areas/toilet areas in general. I class cleaning hamster litter trays as spot cleaning, which is what we should be actively trying to
encourage, not discourage. What we are trying to discourage is
entire cage cleans; i.e removing all the substrate, and/or cleaning all the toys, and/or rearranging the entire set-up at once, etc. All of these events are extremely stressful for hamsters, because no matter how much of a routine you make it, it's removing the animals scent completely and in the case where folks rearrange the entire set up at once, it disrupts the animals routine and familiarity with their environment, and thats why we discourage it. Spot cleaning, regularly cleaning toilet areas, cleaning sand baths etc should absolutely
not be discouraged. I've been in the hamster community a while - 5 years of which I've spent in the natural side of things - and am a huge advocate for natural enclosures and minimised cleaning - but never, ever heard of anyone discourage someone from cleaning litter trays haha. Sometimes cleaning them too much can discourage the animal from using it - but its a rare problem, and I say if cleaning their litter trays daily doesn't cause you any problems with the hamster refusing to use it/picking up abnormal, dirty nesting habits as a result, then go for it!