People are more likely to turn something off and on again than the other way round.

I'm not sure if I'm missunderstanding you and if you're simply asking for an option to turn the tooltip off permantly - but right now it can also be read as that being the default-setting. And in that case its an even bigger NO - people are again more likely to figure out how to turn something off instead of looking up how they can turn it on (specially if they might not even know it exists)

Quite honestly I dont even get the problem - you only see tooltips when you hover over the item and for gear the tooltip actually contains intresting information, does it not?