Well for good of for bad, budgies are kind of dumb. Of course that's compared to most other parrots because they are pretty intelligent compared to other birds and some of the people who own them
But some things that I think makes them hard to own is that they seem pretty unemotional (once again this could be a good thing). They don't seem to care too much for interaction and praise/attention isn't worth much to them. Kili will still do things without food rewards. Even during her free flights I will unofficially recall her when I just want to hold her and she will come and I will hold her/pet her, etc. On the other hand, if Duke isn't hungry, you could forget about him doing anything! I guess he'll still step up but even that is iffy if he's really full.
Also I think the larger parrots pick up on things on their owner better. They kind of become familiar with routines, patterns, where they can go, and things like that. The budgie seems pretty oblivious to those sorts of things. Basically it just seems harder to communicate with it and get through. My Senegal Parrot seems to understand things better.
When it comes to training tricks, the budgie is still capable but many tricks that are simple to teach the larger parrots are very tedious and difficult to teach to budgies. Where this is going is that budgies often require more patience to get to the same point that you can with a larger parrot. On the flipside, the people who get budgies are the impatient little brats who want instant results. Even the "hand raised" budgies I've come across are barely tame at all. What they really mean is that they aren't parent raised but it doesn't mean that they were socialized. A parent raised budgie is usually like $15 and a so called "hand raised" one is $25. For that kinda silly money, no one is going to properly raise and socialize those birds. Maybe if budgies cost $300, they would be raised in a similar manner to larger parrots and be tamer but they still couldn't be any smarter than the species limitations so people wouldn't feel them worth that kind of money. That's why they are a cheap expendable bird that people get for their kid like any other toy and then don't know how to get rid of. The kids get disappointed because they don't step up off the bat and they give up.
If you haven't already read it, check out my article about the abuse of budgies at carnivals as prizes... that will show you just how expendable they are considered to be!
But about that emotional aspect of the birds, it creates kind of a drive. My Senegal knows the difference between me and Kathleen and has specific relationships with people. She likes being around people, she likes showing off, she likes attention and being the very center of it. The budgie really couldn't care less. He'll do his tricks only for the person who is holding millet, otherwise he couldn't care less. He doesn't have any attachments to any person and I'm sure he would be just as willing to live with anyone else. I guess it's kind of disheartening to have a pet that has no attachment toward you so that makes it more difficult for humans to have the budgies. It makes them seem ungrateful.
This is not to say that Kathleen and I do not enjoy Duke but I think it's definitely harder to appreciate the budgie and want to care for it if you don't put a lot of sacrifice into it. Kathleen, would you agree?