That tracks. It does seem like there could have been a list of "213 things Curzon Dax is no longer allowed to do in Federation space", a laSkippy's List.
I'm guessing that's something like, "Anything you might potentially point the gun at, even by accident, is something you want dead anyway, so always keep your finger on the trigger to save time."
I can totally believe that, by the 24th century, phasers are smart enough to fire by intention, not by some crude electromagnetical switch. Triggers are contact points, not switches.
They have technology that can literately disassemble things at the atomic level, from a distance and - even more impressive - correctly re-assemble them. I'd not be shocked if their firing systems had advanced beyond what we have today.
They at least employ such technology with the LCARS displays.
On the TNG episode Hero Worship, Data remarks how simply slamming your hands down onto a control panel won’t actually trigger any of the keys because the surface understands the difference between deliberate finger presses and simple force.
It's hard to see but it doesn't look to me like a trigger of today. I could see trigger in the future being a touch sensitive button that has some other safety features built in.