The reason why it's so opposed I think is because of the fact that it is a competition, and it's not a competition based on any fair or even quantifiable criteria. It's as frustrating as when you're playing a game and there's a "limited edition" item that you want and technically have a chance of getting...but that chance is random and so tiny that you might as well accept the fact it's never going to happen. It frustrates, even when it's just one thing and doesn't really make a material difference.
This really bothers a lot of people. A lot. And for good reason. It can even become resentment -- and again, justifiably -- when people work very hard, they do a good job, and someone better liked by a specific person or group ends up getting the gold ring, maybe with less effort or care. It doesn't make them a bad person, but it does tend to cultivate bad blood between people, and that's not really conducive to a healthy or positive environment.
I've won awards in my lifetime, been nominated, been finalist, and all steps on the way. Pretty much no award ever really means anything; they're just arbitrary distinctions and whoever's organized the award might as well just say "this is a bunch of people we liked enough to give an imaginary distinction," but you know what? I recognize that being passed over for awards makes people feel bad. It makes people feel like they're not doing something, but they never can figure out what that is they're not doing, and that is one of the most frustrating things in the world for any creator.
Even though awards usually don't help a person's career (in fact, statistically speaking, "major" awards are more likely to kill a career), they're still enviable because everybody does like being recognized for doing good work. And yeah, we've got enough distinctions around here that people aren't getting, what with the staff picks, snacks, and so forth. I just don't think it's a good idea to present any further that would just make people upset, or feel unhappy about their work, and the like. It's hard enough creating on one's own terms, whether one wants only to express one's creative voice or one intends to profit off it.
The thing about site-wide, all-inclusive awards is that people don't have the ability to say "please don't bring me into this" and there is benefit in greater exposure to a wider audience, so they probably wouldn't anyway since it's staff. It's much better if it's an independent series of awards and nomination is voluntary, either by someone wishing to recognize the work or by the author.
Ultimately I think, if you want to give out awards, go for it. But don't make it "official Tapastic awards given out by staff" because we already have those distinctions, as arbitrary as they may seem. If you want to give out awards, do the heavy lifting yourself: organize a group of judges, set up an array of criteria, learn critical analysis, and assess any nominations you can elicit from those who wish to participate. It will mean much more and, most likely, be far more positive than something people couldn't really opt out of. It's different when it's a group of people doing their own thing and doing it to help and have fun...and when it's the official staff of a place picking favorites.