My tolerance for donation begging is directly proportional to how A) non-evil the thing is asking for the donations and B) how much utility I get out of said thing. KDE, personally, falls squarely into the "By all means, beg" category for me. I use their stuff every day for free, and their hard work deserves recompense.
I used to feel that way about prominent banners / cards. Then I tried to get donations on my own site and until I became hyper-aggressive I never received even a dollar. It was frankly disheartening. Now, it is not yet sustainable but at least moving in the right direction. In other words, they really have no choice.
I want to see KDE still improving and keeping up in another 30 years. To me it's no different from a telethon for PBS or a poster for Friends of the Library. Intrusive? From a certain point of view, but it pays the bills.