It doesn't have to be unstable, you can feel movement more with a SRW.
I'ts all about leverage and grip. When you've 1,500 lbs or more of pin weight 18-24" above the axle trying to move from side wind, passing vehicles or just the crown in the road, that extra foot of width and 8" more rubber on the pavement on each side will make the TV more stable.
NASCAR drivers always say 8 tires corner better than 4.
I know a lot of people don't want a dually, fine I get that. But you can't argue the physic's of a wider stance and twice the contact patch. You won't find many people with a dually that would go back to SRW for towing. Try it, you like it.