The Morning Thought: Easy ability scores/modifiers

A strange thought with my morning coffee:

With most Old School games we roll 3d6 when rolling abilities. Instead of doing math and writing down the total score for each ability, how about we simply write the modifier? 

QUICK AND DIRTY EASY ABILITY SCORES:
For every "6" you roll you get a +1, but for every "1" you roll you get a -1. 

You roll three 6s, you have a STR +3.
You roll a 1, 1, and a 6, you have a DEX -1.
You roll a 6, 3, and 1, you have a 0 modifier (I always like when people write a +0, as if a zero is better when there is a plus in front!)

Sure, sure, I can hear you saying it already. "A +3?!?! What the hell!?" But really, three 6s? Rarely will come up, and if it does, will that little extra +1 really throw off your game? Also, this is easily balanced off with the possibility of a -3 for an ability. 

ADDED BONUS:
Combine this with the previous post on doing ability checks the Tim Shorts' Way™, you simply add the character's level, add the ability modifier (now conveniently just the modifier) and add those to a d20!