If I could briefly expand this idea...
Someone mentioned that after an air grab, you'll be vulnerable in the same way you are after a triple jump, meaning you can't do anything unless "snapped out of it" or landed. Now, this will already make air grabs a bit trickier to use since the thrown opponent could recover and pummel you.
Someone also mentioned not allowing a downward air throw. This is a smart move because too many combos would come out of it. I do not believe air throws should be open to left, right, and up. I do not believe they should be open to up at all. If air grabs are to work to a fairer extent ("fairer" meaning this isn't full-proof), they should be limited to one direction, and rationally, the opposite would be good. A forward air throw would be too similar to a forward aerial, and an upward air throw would just be dumb.
If the character were to grab, then swing around and release the opponent, the aerial throws could be made to be less broken. The idea of getting out of an air grab, however...
Press a button, perhaps A, if you want to break an air grab. This is similar to breaking a grab in Tekken. If you press A in time, the air grab will be countered and suddenly you will have a split second of priority to strike back. This priority time, of course, is debateable.
As for the throw itself, like I said, it's basically a backwards throw. After it, your character will be in a slump until landing or attack, and your opponent will be busy flying away whatever distance is suitable for their damage. The throw, of course, will not be as powerful as a ground throw since the character lacks the ability to put leg power into the move.
Using this idea, or something similar, the air grab would prevent cheesy combos resulting from downward throws, suicides, kamikazes, edge guards via air grabs (read: forward air grabs), and would discourage players from abusing it due to the aftereffect of using the move. This is the best I can come up with, and really, if it can't be tweaked to work, I highly doubt air grabs would be a good addition to Brawl.