Sorry. I don't care whether an idea was influential or not. All I care is whether someone has a better explanation.
"Do quantum computing folks really think that we are borrowing capacity from other universes for these calculations?"
In this context, your opinion and Deutsch's opinion don't matter. The question is about whether the idea is common in the field or not.
Quantum mechanics is a tool to calculate observable values, and this tool works very successfully without needing to make strong assumptions about the nature of the universe.