Since I discovered this technique I have used it a lot.
It's sort of an alternative to partly muting/palm muting strings, but it sounds a bit different, with a bit of an upper end subtle click, almost muted marimba-esque.
It does require rather precise fretting though, or else you end up with a rattling sound that resembles that of not applying proper pressure when fretting a note the regular way.
It's not about replying a lot of pressure though, but rather getting the position of your fretting finger almost dead straight right, as described in the OP.
And I figure it doubles as great practice for playing fretless bass as well.