It is actually pretty steady - probably the most steady position as allowed by the rules then: no artificial rests or aids allowed (read no Xsticks, wrist rests, even no slings...). That, and the recoil of about 90grs of BP behind a 550gr bullet in a 10 pound rifle. Most of the felt recoil in the prone position is from the comb of the buttstock hitting your cheek, which is completely avoided here. I did try it once with a .22 BSA 12/15 and yes, it defintely can be made to work indeed.
Nowadays, with wrist rests etc being allowed for prone shooting, there is no advantage anymore to the supine position.
OTOH, if you go to Bisley, Stickledown range, you might just see some people still shooting the position, even using Galilean sights - very special!