The problem with flipping a coin for everything is that there is no verisimilitude. Jumping over a puddle and jumping over the Atlantic Ocean are equally difficult and equally easy. So you immediately find that you have the need for more granular rules if you don't want your game to be absurd and potentially meaningless.
Trying to keep us on track; we're not talking about flipping a coin for everything. Here's the OP:
When it comes to a simple does-this-happen-or-not, the GM either knows or isn't sure. If the GM isn't sure, it's probably because the odds of one result or the other are very close to 50%. Why not just flip a coin to resolve it? Is more precision really necessary?
Your example as framed by the OP:
Jumping over a puddle:
NPC succeeds
Jumping over the Atlantic:
NPC fails
The question is: Does the GM need anything more granular than a coin toss to resolve any situation in which they are in doubt?
Being more specific: If the GM rounds everything below 15% (say) to 0% and everything above 85% to 100%, and everything in-between is treated as 50-50, what will break?
For me, I feel it will only really break when the system strongly needs to know the actual results off the dice. For 13th Age it's because so many opposition abilities are tied to the exact dice roll. For Rolemaster, it's because the critical system is so intrinsic to the experience. But for generic degre of success systems, I might argue that the variety of inputs that modify the roll create enough variability that the lack of granularity in randomness is compensated by the abundance of granularity in the simulation/gamist steps.
Essentially, if my orc is swinging with either a +5 or +15 to hit, translating coin flip into d20 language, then the effects of bard song, bless, flanking, height advantage, disadvantage, cover, vision, passion, heroes feast, icon dice bonus, assists, favored foe, tapped aspect, weapon proficiency, defensive posture, berserker fury, magic weapon, divine assistance, and actual offense and defense skills more than compensate for any lack of granularity in the randomness generator.