You don't need to be an 'investor' to invest in Singletrack: 6 days left: 95% of target - Find out more
That little hole you have to stick something in to open clamp. What's it supposed to do? It's a pain in the arse!
Open the clamp.
Is this a trick question?
It’s there so that in the unlikely event of your lever clamp bolt failing, your brake lever will remain attached to the bar. Not any hassle to open it.
It's to o help with installation.
Wait, what?
So all these years I’ve been grumbling to myself, about what’s the point in having a hinge that doesn’t open enough to remove the lever, it’s actually just been user error?
Nope, I refuse to believe it, fake news 
You answered your question during your question! A 2mm allen key works perfectly. Also, how can something that works so simply be a pain in the arse? Need to remove lever? Put something in hole to release clamp. Remove lever. Beyond simple.
I will admit, having never been told of the trick, or read an instruction manual, the seemingly pointless hinge used to frustrate me whenever I had cause to remove the shifters, especially when used with stick-on grips. Right up the point I realised I had to be missing something fundamental and gave the clamp a proper good going over, resulting in one of those great "Eureka" moments. It is a really great bit of design, and as pointed out above means your brakes remain attached should the bolt fail (assuming they are coupled together).
Anybody ever have a brake lever bolt fail?
Not me, but seen someone else's fail and the lever still on but loose. I suppose you could then bodge a trail repair - maybe a cable tie fix to get you home. This bloke was nearly home anyway so rode it loose.
I preferred it when you had to pull-ergh, twist-erfhrgh-pull-argh-streeeetch-bugger it-lift with screwdriver-spray some gt85 under-they'll-never stick again- off your non-lock-on grips, undo shifters, remove them and leave them dangling while you undid the brake lever clamp and pulled it over the end of the bars.. sod it cable's not long enough, undo the v-brake cable... etc.
That little undo brake, poke-a-pick-in-the-hole, remove, system is a pain in the bum! 😀
I'm with you OP.
Ball ache.
APF