Stabilization (placement) of the stones is (yet another) acquired skill. It takes practice.The stone that felt better in my hand ended up wobbling for a while after being placed on the board.
Mr. Iyama v. Mr. Kono.
The stone placements are quite elegant and stable in these NHK TV blitz tourneys.
As Galation mentioned, some folks actually enjoy the wobbling.
I'm greedy: I like both thick stones (10.7 mm) and stable placements.