I found several patents that resemble the L-1011's, dating back to at least the 50s. One such patent remarks that there are two main types, the vane, and the rotating pneumatic tube (also comes in conical shape).
The advantages of the latter when compared to the vane-type are:
[B]etter balancing characteristics, lower air friction, greater sensitivity, and less tendency to flutter or otherwise yield erroneous readings under adverse flying conditions. Also, it requires less power to prevent ice accumulations on a probe than a vane.
A disadvantage is keeping the moisture/dirt out:$^1$
There is one difficulty in making this a rugged instrument. The movable cylinder must be mounted to move as freely as possible so as to have good sensitivity. This requirement makes it difficult to make a good seal around the moving cylinder to keep out dust and moisture.
A motor would solve this seal issue. But the advantages of the form should hold whether motorized or not. A more recent patent uses the tube design to combine the AoA and static/dynamic pressure sensors into one probe.
Was it used on any other aircraft besides the L-1011?
The F-14, for example, uses the pneumatic (conical) type:$^2$
(primeportal.net) The left (port) side of the F-14's nose.
$^1$ https://apps.dtic.mil/dtic/tr/fulltext/u2/102442.pdf page 50.
$^2$ The location is confirmed by the F-14D manual (only 1 probe), and it's referred to as probe (not vane).