By no means it does not apply to Bruce alone, the concept that these meta humans and DemiGods are afraid of mere human is absurd, and the humans could be allies or enemies. Its absurd that these supervillains cede command to Lex or are scared by him. Just as its absurd that human villains can scare superheroes or go after them.
My point was that Bruce being the mastermind of the team, that he plans with foresight is what makes him a valuable asset to the Justice league. Although sometimes the paths he takes is questionable.
While HQ being on same league makes no sense. Bruce brings alot to the team, what does HQ bring so valuable to these meta humans and Demigods for her to hang around. Besides Superheroes who adhere to such high principles hang with a sexual harasser? What does she has in common with WW, Superman, Flash?
As for Bruce not being praised by his fans on the internet not being true, I don't agree. You can't take this forum as measure of standard. Something I like on this forum is that it groups many people together, with different opinions, discussions can be engaging and interesting, others less so. I noticed that you can find lots of fans interested in characters that usually you don't find that much about. Just see the number of thread pages for certain characters, you might be excused if you think that they are the most popular characters around. It is also a moderated place, that has order, not free for all as on other social media. So we can't say because on CBR forum you don't find that, it does not occur outside this forum.
That batman might generate more interest or controversy is natural, he is one if not the most famous DC character. But that Part of his fanbase are saints is not true and that applies to all fanbases for fairness sake. The most annoying things however if you express a concern, or disagree you are labelled an envious whiner, when people who write that just don't even try to understand that concern.