I suppose often the view is that they're doing you a favour taking the unwanted stuff off your hands, so why try to be polite or try to persuade when you can just ask for a time it can be collected.
Yes, I've concluded this as well. They have the line of 'keeping out of landfill' but that is not because it's useless rubbish that unfortunately now needs to go to landfill, but rather because it is good, useful stuff that you personally no longer have a need for.
They are benefiting just as much as you, otherwise they wouldn't bother collecting it from you. Your bin men wouldn't dream of emptying your bins for fun and giggles and to find the valuable treasures if they weren't paid to do so!
I tend to find that rudeness like this goes hand in hand with a clear inability to see things from anybody else's perspective. Because they wouldn't dream of giving something decent away free, just to do a stranger in the community a good turn, they assume that you're probably lying when you claim that it works properly and are just trying to scam somebody into taking your broken/hidden-damaged rubbish away under false pretences - which is probably exactly what they would do.
All you can do is to prioritise the polite ones. Contrary to what a lot of people think, you are under no obligation to give it to the very first responder.
I wonder how many of the rude people realise how much stuff their rudeness might be costing them, when their "Mine - coming for it tomorrow" is ignored in favour of the "Hi, is this still available, please? If so, I could collect it tomorrow, if that works for you?" that comes in an hour later.
It's not even just a case of not wanting to reward rudeness: in general, the polite people are far more likely to actually turn up and collect the stuff, as they've taken the time to treat you like an actual human offering something that they genuinely want, rather than a faceless commodity to exploit before taking their time to decide if they really can sell on do want all of the items that they demand as soon as they are posted.