OK, you asked about a sway bar.
I tow a 35.5 foot > 10,000 pound tandem axle travel trailer with a 3500 diesel Chevy long bed dually. I use a weight distribution system with built in sway. I use the Equal-i-zer 4 point weight distribution system, rated for a 14,000 pound trailer and a tongue hitch weight of 1400 pounds.
Would I tow this without WD and sway control.... NO! I tried it and didn't like it.
An aftermarket friction sway bar is better than nothing at all. But you definitely want some kind of sway control, long or short trailer.
The problem with the aftermarket friction sway bars is the fact you really should remove them every time you back up. This can be a real annoyance.
Why remove them? If you back up, you run the risk of bending them if you begin to experience a jack knife. Also, there is a risk the little ball on the hitch head could break off. This would ruin your hitch head too.
What you really should consider is a weight distribution hitch system that has built in sway control. Equal-i-zer 4 point, Blue OX, Reese Dual Cam. This way you won't have to worry about that extra friction sway bar.
Yes ..... you need sway control, whatever system you end up with.
This coming from a dually 1 ton driver with a 35 foot trailer.