Honestly, this is as much a ventilation and housekeeping issue as anything.
I volunteered at a rescue that had 350 birds, and a large precentage of them were large toos. Needless to say, there was a lot of (daily) cleaning involved.
What happens is that long term exposure to excessive amounts of dander (and dried feces - that would be EVERY bird, not just the dander birds - don't kid yourself) leads to an unhealthy level of air quality. The dander particles get into the lungs, and over a period of many years, become a lung irritant, leading to breathing problems later in life.
The solution is fairly simple: keep the birds in a well ventilated room, bathe dander birds frequently - at least once per week - preferably daily mistings, weekly soakings, vacuum, dust, and clean cages sufficiently often enough that the dander is not allowed to accumulate in significant amounts.
i.e. do the housework that comes with owning a dander bird - or any bird for that matter - but most especially the dander birds.
Most folks clean up because simply because it's disgusting if you don't. If you have a fairly large number of dander birds in the house, it's a health hazard.