That's unbelievable. Are you saying these sweaters will just disintegrate a little bit with every use? They might as well be garbage to me then. I expect a sweater to last for years. What affordable, better quality alternatives are there? Should I just stick to 100% cotton if shopping in this price range?
And if I am stuck with these sweaters for now, how can I minimize the annoyance of using them?
Basically, yes. There's a reason those sweaters are so cheap, and I wouldn't expect to get more than a year, maybe two, of use before they start pilling substantially, getting holes, etc.
Good wool is not cheap. Good cashmere sweaters, even less so--good cashmere sweaters start at around $500.
Not sure what your budget is to suggest alternatives. Johnstons of Eglin on Sierra Trading Post is usually a pretty good deal depending on the budget though.
As for now, washing isn't going to do much good, so I'd just get a good lint roller and use it after wearing.