The problem people have with Kendrick is definitely the way he is covered by the media - in particular, i think, media outlets which historically have never had much time for hip hop before mbdtf "transformed" it into a "legitimate" artistic medium. (I mean, they still don't really respect it which is why they push the narrative of Kendrick as a "writer" rather than a "rapper").
These media outlets aren't merely content to hand him hip hop's crown (which is irritating enough because they don't have any credentials to support their role as hip hop kingmakers) but are constantly trying to elevate him to be some kind of leader of my generation. But I don't, and does anyone, actually know who Kendrick is and what he stands for? What exactly is he leading? The message in his music is obfuscated by meandering lyrics and the vaguely defined tenets on which tpab and damn are built just seem to be a repetition of the sort of views held by any left leaning person. Where is the radical position in his music? Where is the challenge? Oh, you wondered why he can sell so many records...?
He makes good popular music with lyrics that sound like they might be deep or something because they are weird and don't properly make sense (Hov already dealt with his type - just cos you don't understand him, it don't mean he nice, it just means you don't understand all the bullshyt that he writes) and with a political stance that's vague enough that a sizable spectrum of political views can feel validated by it.
I wish the media could just leave it on the "we really like how his music sounds"-level rather than think-piece-projecting him to a platform he is not cut for.