Hogwash! You're being "pitched".
First, there has been some implication that adding mass to a headstock improves sustain. Well, a locking nut adds mass. Second, there has been some implication that rigidity and stability at any string block (like a nut) improves sustain. Well, a locking nut is certainly more rigid and stable than bone or graphite. And third, we are only talking about open notes here. Once you fret a string there is little, if any vibration of the string behind the fretted note. At that point the fret becomes the string block and the nut is moot.
And consider this. Locking tuners are VERY good at eliminating slack from peg windings and any shifts that might occur with trem use, but they don't do a thing for slip and slack at the nut itself. Ergo, Floyd type bridges usually use a locking nut for better accuracy returning to pitch after trem use.
For something like the stock Strat type bridge where you won't be uber bending and dive bombing I think the locking tuners are a good choice. They're an improvement and they don't change the stock instrument significantly. But if I'm whacking the trem and dive bombing with a Floyd I'll take the locking nut every time.