Considering it only diverges from the standard Gregorian for dates more than 400 years ago, it's not super relevant. Most people don't think about it. But it made a lot of sense to do the shift at the time. All recorded dates up to that point had been physically written down, so it would have been infeasible to migrate those all to the proleptic. If computers had been around, maybe things would have been different.

Fun fact: Greece was still using the old Julian calendar as of 1928, so it's entirely possible that you'll see dates on relatively recent Greek documents that are up to 14 days off from the calendar the rest of the world was using. Civil timekeeping is just a mess.