I recently came across an English learner saying that 12/12/12 is the last time such a repetition of day/month/year (or month/day/year, or year/month/day) will occur in the Gregorian calendar for a long while "Because 13/13/13 wouldn't exist."

I don't know whether "couldn't", "can't", or "doesn't" would the best word to use, from a prescriptivist perspective.

Based on personal recollection, I assume "can't" would be suitable for a real object that is unable to do something:

My car can't start

Or you could use "don't" for something that's possible, but doesn't happen:

I don't travel via the tollway.

But the problem is that 13/13/13 is not like a car. As well as being an abstract noun, it's also a logical contradiction. Does that mean I should use a subjunctive?

Assuming that "couldn't" and "wouldn't" are subjunctive, this answer seems to suggest "couldn't" would be a better fit than "wouldn't", as it's an "Equivalent of "can" (possibility)".

Also, what would be the most common expression from a descriptivist, as opposed to a prescriptivist, perspective? Based on a google search of "13/13/13 * exist", it seems to be "doesn't" - does that sound plausible?

I recently came across an English learner saying that 12/12/12 is the last time such a repetition of day/month/year (or month/day/year, or year/month/day) will occur in the Gregorian calendar for a long while "Because 13/13/13 wouldn't exist."

I don't know whether "couldn't", "can't", or "doesn't" would the best word to use, from a prescriptivist perspective.

Based on personal recollection, I assume "can't" would be suitable for a real object that is unable to do something:

My car can't start

Or you could use "don't" for something that's possible, but doesn't happen:

I don't travel via the tollway.

But the problem is that 13/13/13 is not like a car. As well as being an abstract noun, it's also a logical contradiction. Does that mean I should use a subjunctive?

Assuming that "couldn't" and "wouldn't" are subjunctive, this answer seems to suggest "couldn't" would be a better fit than "wouldn't", as it's an "Equivalent of "can" (possibility)".

Also, what would be the most common expression from a descriptivist, as opposed to a prescriptivist, perspective? Based on a google search of "13/13/13 * exist", it seems to be "doesn't" - does that sound plausible?