So, I own a P85+ and currently have the 19" rims (slipstreams) with the Goodyear Grand touring tires on it (i.e. NOT a performance tire). This car puts down more power than the current RWD Model 3 (it is heavier though). The only time dry weather traction is an issue is when really nailing it off the line. The worst case scenario involves turning from a stop to merge onto a road with fast moving traffic. As an example, I turn from a side street onto a freeway frontage road regularly. In addition, the side street I am turning from has "decorative" brick pavers in that intersection and, when wet, they offer even less traction. Still, even then, it is just rarely an issue. The S puts down its power so smoothly (relative to other high horsepower RWD cars I have owned) that it rarely breaks traction, or if I think it will, I can ease out a bit and still nail it once the car is straightened up with minimal issues.
From everything I have read the torque "hit" off the line in the Model 3 is softer than the Model S which would make the dry weather traction even less of an issue. Now, I have driven a P85D loaner (21" PS2s) and, just a week ago, had a new 100D loaner (19" Goodyear tourings). I will say those cars were even more surefooted than my car. The 100D in particular allowed me to hammer it more from a stop into the turn onto the fast moving traffic road, but it was a "nice to have" vs. a "must have" in fair weather and even "normal rain" driving (here in Texas anyway). The really high horsepower cars (P85D on up) need it to put all the power down.
I suspect folks who live in states with a lot of snow or frequent rain might have a stronger preference for dual motor (I probably would).
One other downside to dual motors - front motor whine. It's noticeable on the dual motor Model S and I suspect will be even more so on the Model 3 (seems like you are closer to those front wheels in a more cab forward design on the Model 3 and it may have less sound deadening than the latest Ses to boot).
Oddly enough, the most noticeable benefit I saw with that recent 100D loaner (which we had for a week) - increased regen. I immediately commented about how the car was closer to "one pedal driving" than my P85+...a nice perk I hadn't paid attention to in my prior drives. Still not at Chevy Bolt or early BMW i3 levels, but noticeably stronger than my RWD car.