Any bike with a fork mounted fairing is going to begin to wobble at high speed. The fairing is, for lack of a better term, an Airfoil.
Of course there will be many variables, i.e tires (ground contact surface), suspension, crosswinds etc. that will make every bike react different at various speeds.
If you're going over a hundred miles an hour and your tire comes off the road, albeit, ever so slightly, then your bike is essentially an airplane...and as such, the fairing acting as an airfoil, is now in complete control.
Very few bikes in the motorcycle world even have fork mounted fairings! Most are frame mounted and all of the Superbikes are...
If you have a friend with a Road Glide try this, go out to the interstate and pass a semi with your bike at high speed, then try it on a Road Glide and you’ll be a believer.
With all that said, be very carful going fast with any fork mounted fairing!!!!
I had an old Suzuki back in the 80’s that I took to 125 and the handlebars were almost slapping the stops before I could get it slowed down and recovered.