I don't see any reason it would be technically unfeasible.
You could give everyone a slider-based matching bonus value that is proportional to their selection on the slider (with the better team balance end of the slider giving a bonus of 0, or a negative amount, depending on how you want to set it up).
Example A:
Then, if you only want to put people in matches of equal or better game balance than their individual selection on the slider, you could just cap that bonus value for a given combination of players for a potential match based on the minimum of their individual bonus values (so, if you're matching 4v4's with 20 people in queue, the bonus value used for a given potential match would be the lowest bonus value of the particular 8 players in the potential match that is being considered, and a different value could be used when evaluating a different set of 8 players within the same matching cycle).
Example B:
Alternatively, if you want to not restrict in that way and make matches more likely if anyone wants faster matching, then you could do the same thing but not restrict the bonus value to that of the minimum, but instead make it equal to that of the average of the set of players being considered for a potential match. That could put people in matches of better, equal, or worse game balance than their individual selection on the slider, but it would factor everyone's individual preference in with equal weight.
I think either of those systems could be better than what we have now.