This would be very simple to do from the S1 team. They just need to "clean" up more when you press STOP. Pressing Stop in S1 looks it just pauses the engine, or maybe some note off messages.
Try this scenario. Press Start/Play and just keep pressing one note in your keyboard, now press STOP, some instruments stop, some don't. That's because some instruments are doing the "cleaning up" in the way they are programmed, others they keep playing until you let go. The same scenario in Cubase would stop EVERY instruments, because Cubase is sending some notes off, midi cc123 or I don't know what.
That is why Studio One has more hanging-stuck notes than other Daw's. Pressing STOP should stop everything and I believe this is a veeery easy fix by Presonus team.
I've assigned one of my knobs in Kontakt A61 to act like midi CC123. Thats the only way I know how to fix this issue. No more Kontakt problems, just select the track move the knob, stuck note is gone.
Since my problems are all related to Kontakt a shortcut to (!) Panic Button would be ideal but that's up to Native not S1.