The way I imagine it is like the calendars are both rulers that are slightly off from each other. We were using one ruler, and at a certain point we went from using one to the other, so our "present" was never mapped to those dates. But you can represent any point in time as any of those calendars, like we can represent a specific temperature as Fahrenheit or Celsius. The calendars extend forwards and backwards to infinity.

It's not a wrong way to think about it. There are some use cases for proleptic calendars, but there are just as many where it's completely inappropriate. If you ever need to compare what day you think it is with what day someone in the past thought it was, then yes those dates don't exist in any real sense.

I wouldn't say it's it's straightforward to convert between them, either. The Gregorian calendar was first adopted in 1582, but the UK and it's colonies didn't follow suit until 1752. Russia didn't convert until 1918, and Greece didn't switch until 1923. We're just over 100 years out from active use of the Julian calendar. So you have to know who the speaker is and where they are or where they are from to know what they mean.

Since these places switched at different times, they had to skip a different number of days. It was 10 in the 16th century. It was 13 in the 20th!

If you're reading a journal by a British man who lived in Russia through the end of the Great War and then moved to Greece in 1920, what does he mean when he's talking about a lunar eclipse he just witnessed?