There is absolutely a reason to vote "None" sometimes in solo queue drafts.
Your ban choice is often a signifier of what lane you plan to play.
This can give information to the opposing team about where positions are in the draft order, and who is able to counterpick the opposing position.
By denying this information, you make it harder for the opposing team to plan their composition, particularly before your own champion choice is revealed.
It's rare that the utility of this strategy outweighs a ban against your worst matchup - but I've seen it used effectively, and done it myself before when on a particularly meta-favored champion with relatively few bad matchups.