Correlation may not equal causation, but the data isn't on your side.
The US has an inordinately long election process that people hate. Our neighbors to the north, and our chums across the pond, both have far shorter election processes and greater turnout overall.
There's a study I'm looking for that further corroborates this idea, but I cannot find ATM. Hopefully, I can post it sometime in the near future.
I think the greater turnout in Canada and Britain has more to do with the fact that they have more parties to choose from and the range of political ideas up for debate is wider. In continental Europe, turnout is even harder, and I would guess part of that is due to the fact that they have proportional representation, meaning nearly everyone's vote actually counts.
That's not to say the long drawn-out process isn't part of it, but there's a middle ground between the current system and consolidating all primaries to one day.