I'd feel bad for the fans, but idols are human and I don't expect them to love their fans all the time
I'd be really gulible to assume they haven't complained about us at some point, especially when they are frustrated or in a bad mood. As long as they don't go out of their way to let it be known that they think low of their fans, let's normalize idols having thoughts and opinions that aren't all sunshine and rainbows 24/7.
As for the letters, unless they throw them away right in front of them, I don't see the issue. They don't have unlimited space, especially if the person in question is very popular and prone to getting a lot of letters.