It would appear the damper was fitted to the SV1000 only because the TL1000 was a bit of a handful.
In general bog standard damper will meke turning the bars "stiffer" Once they get worn they lost their consistency so will be stiff on part of the travel and free running on others or even stick in places. Mine had all sorts of problems including air in it so it was jerky as hell. I since cleaned it up and replaced the oil and it's a lot smoother but not refitted to the bike.
Imagine somone randomly turning up and down a stiffness adjuster on your handlebars and that's what mine was like. All kinds of random front end behaviour when in bends and weeesh wooosh noises when doing 3 point turns.
Took it off and it all handled a lot lighter and far more consistently. Got some feel back from the front wheel when in bends and could feel the front end going light under power all of which were missing when the damper was fitted.
So far as I can see, unless you are a ham-fisted lunatic or have oodles of power a damper is just bling and bling that hampers your handlling in my experience is anything to go by.
If I get a tankslapper starting, I simply pull a wheelie, let it settle down. put the front wheel down then complete the overtake as if nothing had happened*
See the guy at 1:17 in this video for a "how-to"
https://www.youtube.com/watch?v=xzB6KSlD6ec
However, if you fancy fitting or retaining a damper then feel free to do so just make sure it does not get jerky.
Cheers,
*yea right! Personally I don't ride like a ham-fisted lunatic.