The GM's job is to do more than to follow the rules.
That is why we play tabletop, as opposed to CRPGs.
It is appropriate, hell, even called-for, for the GM in shadowrun to add negative qualities when things happen in-game to justify it. Not only does this mechanically tie the character's sheet to things happening in the game, add a burden for them to struggle out from under, and show that their actions in the game do affect their characters and the game world, it adds an extra edge beyond just 'dying', 'staying the same', or 'getting stuff' to the outcomes of their actions.
These are, for me, the reasons to include this in your games. Not only are Shadowrun negative qualities tilted to be more than just a random negative number or a huge 'YOU'RE SCREWED LOL' like in some systems, but rather to be interesting and create interest, by forcing the player to bypass or deal with more problems, problems that tie directly into their character's past. But what you're really here for is the boost to verisimilitude, which is huge, and in my mind, verisimilitude is what gets people involved in and interested in the game. There's nothing you want more.
Does adding negative qualities lead inevitably to a grimmer, grittier campaign (to the point where characters are just stuck with a bunch of them they can't get rid of?). Back your answer with actual experience please.
I've played three decent-length Shadowrun games. In all of them, qualities were awarded, both positive and negative, on an ad-hoc (non-karma-based) basis. All of them were improved for it. When one character got paralyzed from the waist down, it added to the game. The key was that the GM wasn't handing out negative qualities as punishments or to push some agenda - they came up organically during the course of play.
I was a player in all of those games. In two of them, I played characters with more negative qualities, right out of the gate, than were allowed by the creation rules. In one case, significantly more, something like 4x. I'm a pretty experienced roleplayer, I guess, but the GM did not stint in his job to use them to screw me as much as he possibly could, and honestly, I loved it. My character was cacked on, built relationships with the rest of the team through them helping her out of fixes, was useful despite her flaws in a way that if i'd just been useful would not have been anywhere near as good as the story, and in the end went out in a blaze of glory to save the rest of the party and a good portion of the western coast of the united states; and when she did, it meant a lot more given how hard she'd had to work to get out from under the crap.
But the main thing is just don't take lots of stacking global negatives to dice pools. Other than that, it just... adds to the style. Shadowrun is dystopian cyberpunk. If you're not messed up and being shat on, it's not.. appropriate for theme. Negative Traits just give the GM guidance on how to crap on you, and when to fill the crap full of razor blades.
And hell, it worked out for me. I have honestly played very few characters that felt as real as that one.