Relying on a steering damper for this would be treating a symptom caused by improper operation on the bike. Treat the root cause and loosen up on the bars.
Allow me to share an anecdote: I hopped on the freeway the day I got my first bike. I just kept repeating the MSF training mantras to myself (push right, go right; grip the tank with your legs) and did fine. It wasn't until the next few freeway rides that I started feeling the 'wind effect' a bit more, but I just rode it out chanting, 'stay light on the bars. Stay light on the bars.'
The 'moment of truth' was going over the San Rafael bridge for the Sunday Morning Ride within the first month of riding. That bridge is
long and
windy. The mental trick I developed going across? 'Stay calm. If you panic, you
will fuck up, and something bad
will happen.' So I dug into the tank with my legs, stayed calm and happy, and everything was chill.
In a week or so of regular freeway riding, you won't even notice the wind or rain grooves anymore.
The best part about learning the 'lower-body anchor' technique and keeping your arms light is that even when you go over bumps, rain grooves & other road hazards, even while leaning is this: you'll feel the bars shudder, turn in a bad way, then come right back where they're supposed to be all before your conscious mind has time to think of what to do. Your bike knows where to go. Keep a light touch and trust it.