-A mixed attacker can effectively hit physical/special walls/tanks, though they still have a bit of trouble against mixed walls/wanks.
-One reason to use a mixed attacker in the first place is for more coverage options, so using a mixed set could help a Pokemon hit more types super effectively.
-Letting a Pokemon used a mixed set usually allows more opportunities for a Choice Scarf/Assault Vest, two fairly good items (Tangrowth is notable for using a mixed Assault Vest set).
-Mixed attackers make better use of Growth on sun teams (Venusaur and Shiftry are notable Growth users on Sun teams).
-It isn't very efficient to max out 2 attacking stats since usually you want to max out speed on a dedicated attacker (unless you're using a Pokemon that Speed EVs won't help its bad Speed). This means you won't be able to hit as hard physically and/or specially as you would if you had just stuck to one category of moves (for example, a 252 Attack, 4 Special Attack, 252 Speed EV spread allows a Pokemon to hit as hard physically as it would on a physical set, but a, let's say, 128 Attack, 128 Special Attack, 252 Speed set would be cutting into both of your offensive stats).
-Natures will usually cut into your bulk for the sake of boosting your Speed/Attack/Special Attack, which just isn't as practical as Jolly/Timid/Modest/Adamant. While this isn't a problem for Pokemon with very low Defense/Special Defense (Hasty and Naive, respectively), it can still be a problem for some Pokemon.
The cons of mixed attackers are pretty big, as Natures/EVs are very important in competitive play, and failing to pick the correct Nature/EVs for a mixed attacker will happen a lot. I will say, some Pokemon can run Draco Meteor sets with 2-3 Physical moves and it works well for that specific Pokemon.
So, that's what I've gathered so far.
Hope this helps! :)