This is an incredibly troubling aspect of the push toward a cashless economy. Not only does it marginalize the unbanked (those who can't bank due to illegal immigrant status, or other mitigating circumstances), but it's also an incredibly powerful tool for population control.
It removes the agency a modest savings give us, by concentrating all wealth under the control of a select few anointed conglomerates. It also allows onerous policies like negative interest to be a new, truly inescapable regressive tax regime.
Edit: notahacker makes a compelling point that negative interest is likely less regressive than inflation. I thought it was something worth bringing to the root of the thread.