I think it likelier the cost saving will mean NO reminders!
If that did happen,at the very least ,we wouldn't be expecting reminders and therefore more likely to put it on our to do list,however as you know we do expect them and therefore wait until we get them to pay,and if we don't get them,we forget.
Also surely if we don't get reminders ,there is a saving to be made in terms of staff,postage etc,and maybe,though I doubt it,that money could be put to better use