Unused data is risk without offsetting value
A field collected because it might be useful someday, but never actually used for anything, adds to what a future breach could expose without adding anything to what the system actually does. Data minimization asks, for every piece of data a system holds, whether its stated purpose actually requires it — and treats 'we might want it later' as a reason to reconsider, not a justification to keep it.
This isn't primarily an argument about storage cost. It's about the fact that every piece of data retained is something an access-control policy eventually has to account for, correctly, indefinitely — and a system that holds less data has fewer places for that policy to get something wrong.
Minimization and access control are complementary, not substitutes
Reducing what's collected doesn't remove the need to control access to what remains — the two are separate, reinforcing strategies rather than alternatives to each other. A system that minimizes aggressively but still gets access control wrong on the data it does keep hasn't actually reduced its real risk by much; minimization narrows the target, it doesn't replace the guard in front of it.