My experience, after almost 25 years of observing random stat generation, is that players claim to prefer random generation until they roll a substandard character. (With "substandard" being relative. If the player's PC's got stat-mods totalling +4, but another player's PC has stat-mods totaling +13, the first player is going to -- rightly -- consider his PC substandard.)
Then typically one of three things will happen: (1) the player will "suicide" the character, in order to try again for "random" high stats; (2) the player will wheedle, cajole, and whine to the DM, again in order to try again for "random" high stats (or, although it's not the player's ideal outcome, a chance to retroactively bump up the stats he rolled with his "preferred" random method); or (3) recognize the merits of point-buy.