Like all quotes, on first glance it appears insightful and impressive, but a closer second look reveals it to be nonsense.
> Nothing in this world can take the place of persistence.
Luck and circumstance can.
> Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts.
The world is also full of persistent failures as well.
> Persistence and determination alone are omnipotent.
The Axis powers in ww2 were as persistent and determined as the allies. You could argue they were even more persistent and determined. They failed. Has there been a more persistent and determined presidential candidate than Hillary Clinton? She failed twice. If persistence was all it took, Hillary would have been president.
People love to pat themselves on the back for their successes. If coolidge was born into a black family in the 1800s rather than into an elite new england family, I wonder how much persistence and determination would have mattered.
Persistence is an important characteristic in life, but there are far more to success than persistence.