The solenoid plugs off the main jet
On some carbs they will continue running on the idle jet
So it does not affect fuel coming into the carb, it stops fuel going through the main jet
If for instance if the float needle is not cutting the fuel off then the bowl will over fill & fuel will enter the engine via the float vent hole
This of course looks like very rich running and can take anything up to 1/2 to come into effect depending upon how much fuel the engine is using and how bad the float needle is leaking .
That one took months to nail down but after that pressure testing float needles became SOP ( you don't fool me twice easily ) .
Now because there are governed engines, the throttle control you move does not directly control the throttle butterfly in the carb
All it actually does is set the upper limit of butterfly opening
So when sitting there the butterfly could be open say 10%
When you start to move & put a load on the engine it will open another 5%
But when you turn the blades on and put a big load on the engine, the butterfly will open as far as it is allowed to .
If you have a fuel blockage or air leak then the engine should surge and that surging can be reduced a little by closing down the choke a little
As your engine just cuts out I am tending towards thinking you have too much fuel
Running fine on low throttle settings where the fuel is being supplied mostly via the idle jet then spluttering & dieing when the throttle is fully open and the main jet supplies the bulk of the fuel is exactly what happens when the main jet is way too big ,loose or missing all together .
The latter is very common with the Nikki carbs that have the plastic plate as it gets blown out during cleaning and if you don't know it should be there, you don't miss it .
On the twin barrel carbs the main jets are held in with just the O rings so regularly fall out but in this case you see them when you pull the carb apart .