Failures happen on a roll of 1, 2, or 3 without buying any upgrades to remove them. On a d6 this gives you a 50% chance of failure, which goes down as the die gets bigger. Additionally, a bigger die gives you more space to add successes.
That said, nothing forces you to upgrade your die size. You're welcome to stick with d6 if that's more fun for you or you care about an "optimal" experience, for whatever that means to you.