I agree with you. And, IMO, when any of them are neglected, as in not getting enough one-on-one attention, then that's "too many" (hoarding is a different matter; it is a psychological disorder that involves gross neglect and a pathological lack of empathy for the animals, and it becomes actual hoarding when it becomes overcrowded, dirty and unhealthy. It is hoarding if the animals are suffering in any way).
But, IMO it can still be "too many" even when it's not hoarding, and that's more subtle and hard to pin down. To me, "too many" involves psychological neglect, lack of toys, lack of proper dietary variety and health care monitoring, just general slackness in individual care caused by the caretaker being spread too thin. I'm also going to go out on a limb and say that if the birds are more "possessions" or "collectibles" in any sense, and not "beings" or "individuals," then that's "too many" even if they have food and clean cage trays. IMO "too many" is often a function of "collecting." I don't regard birds as collectible items, but some people seem to. They will get a bird because even though they have plenty, they wanted a p'let or a quaker, or even a macaw, of another color. To me, birds (especially the larger species) are more like kids, and you don't have a kid because you're hoping it'll be blonde or have green eyes (hopefully). I'm not saying all households with multiple birds are bad. If they're getting plenty of attention and toys and health care, then a multi-bird household is fine. But, I do not like to see households where the birds seldom leave the cage because there are too many for the caretaker to manage and monitor.
If I'm totally honest, with six, I find that there's usually someone who didn't get as much attention during the day as the others. Someone always seems to come up a little short. And, to me, that's not right. Even my little guys love attention. Corbit loves to sit on my shoulder and say "hi sweetheart;" he loves when I handfeed him millet and tell him what a good boy he is. He loves kisses. I don't want to be the person who doesn't do that for him because she got a bunch of larger birds and so he got shunted aside. IMO, none of them can reach their full potential if they're not getting some attention, even the hands-off birds. Even those birds need proper monitoring and proper care. They need toys and supplies, and they need dietary variety, etc. All that takes time. If you stop and say, "in all honesty, what would this bird's life be like if he were my only one?" and if you know the answer is drastically different from the way his life is now, well, then that's "too many."
So, six is my limit. Proper cleaning, diet and health care, and interaction, would suffer far too much in my estimation if I had more. And that's not even considering the expense, which is always an issue--especially the vet bills.