Imagine for a minute I am a an extremely powerful mythic hero and I enter a thorp of 50 people. Average farmers, bakers, cobblers, good wives, etc. I institute a policy that I will train every one of them to be an adventurer and eventually reach a level where they can do an impossible task. (Cleave a mountain, divert a river, swim up a waterfall, etc). I have the power and resources to train them all and keep them alive until they reach said level. Additionally, they are slavishly devoted and will do everything in their power to accomplish this goal.
How many of those 50 people will be able to accomplish that impossible task? One? Ten? All fifty? Zero?
The answer you provide is essentially my concern with this system. If everyone is able to do impossible things with sufficient time and devotion, then the world should be full of people doing impossible things. Not everyone, but lots of them. If we say not everyone has the spark needed to reach that level, then we have to say why. Is it genetics, magical aptitude, supernatural blessing? Why are some able and other not?
Hercules is mythical because he's the only person in ancient Greece who can do that kind of epic stuff. There are other great heros, but none of them can divert a river. Jason is favored and Odysseus clever, but neither are matching Hercules in power. He's got some great parentage to thank for that.
Which returns me to my original question: how many people in that thorp have the potential to be Hercules?