Also the air space at the tip moves the CG rearward reducing the momentum of nutation or tip wobble.
Ayup! All about getting the run of bullets to fly right, which is all that matters for target use.
The shorter cylinder of the mass inside the jacket cuts down on the wobble and on the length that the mass is, effectively. At the hundreds of thousands of RPM (12 twist barrel, at 3000 FPS, equals 180,000 RPM!)that they turn at, any change that can be made to cut out the wobble, will increase accuracy potential.
For target or accuracy shooting, nobody is having to worry about reliable expansion.
A short fat mass is more stable in the spin, but not as streamlined. Adding a long closed in hollow nose streamlines it without adding much to the rotating mass effective length.
As to what the Snipers use, they use what has been issued and approved by more Lawyers than you might imagine. Boils down to using bullets that were not designed to cause suffering, they were designed to fly more accurately. They are not allowed to modify ammo, and they are not allowed to use ammo that is not approved for use. Not Geneva Convention, another whose name isn't coming to me right now...