Starting from a late 10.12 release (to stay within a Long Supported Release (LSR), I'd recommend 10.13), the auto-checkpoint behaviour changed to not create 'user checkpoints', but introduce a new category of 'confirm checkpoint', that is always named 'auto-confirm-backup'.
That one always over-writes the former version, so the counter keeps at '1'.
This should solve the problem of filling up the user checkpoint list by just running the auto-checkpoint feature.
With regards to 'user checkpoint' deletion in general: It seems there is no way to do so via API.