I can't think of any environment that I've been in where this is true. I think the closest I've been was as part of a team of three people where each of us could really handle any task in the codebase. It was also true that there were things that we each cared far more about as individuals, so, in spite of comparable skills, we tended to gravitate to specific stories, anyway.
As a manager, I have every expectation that we won't be doing scrum exactly by the book, but that's totally fine. I'm more concerned about (reasonably) consistently reproducible levels of productivity, not squeezing every point out of a sprint. If there's slack time, great. That seems to be when people are most likely to contribute new stories, learn something new, etc. Besides, rigidly following scrum feels anti-Agile, anyway. People and interactions over tools and processes.