That's why allowing the data to be replicated is so important if you care about preservation. It only takes a few happy mutants who think some otherwise boring data might be interesting and keeping a copy for themselves.
Again, you're assuming that ordinary people had some way to easily "keep a copy for themselves". This was emphatically not the case. This data was not digital. It only existed as a set of magnetic tapes in an unusual format: 1" magnetic tapes containing application-specific analog data. The number of institutions that would have been capable of copying and storing this data would have been small; it's improbable that any individual, "happy mutant" or otherwise, could have done so at the time.
The notion that any sort of data is easy to copy and store is a modern concept. It was usually not the case in the past.