I wonder how useful more than 4 digits would be. Once our species has achieved interstellar travel, we'll probably use a completely different representation for time.
By default, ISO 8601-1:2019 does not permit negative years in date representations.
Expanded representation (i.e. five digits or more for the year) permits both positive and negative years (and the sign is mandatory for both positive and negative years).
ISO 8601-2:2019 has provisions for numeric extensions. Subclause 4.4.1.2 permits negative four-digit years (years -9999 to -0001).
Note that both of these options require mutual agreement.
One use: I was teaching some developers COBOL, and I wanted to illustrate for them how the Y2K bug came about.
So I gave them a project to do parsing a file with contemporary dates in. Then towards the end I quietly supplied them with a similar file containing dates from the year 10000+.
Whether or not the devs of years past felt it similarly unlikely that their software would live to the year 2000 as we do the year 10000, I don’t know. But it was a fun exercise!
Don’t forget that when Y2K problems were being created the hardware was _way_ less performant than the hardware of today. There was a reason to be wary of how much memory you are using, now there isn’t much.
All experience thus far suggests "No." We'll be using all of these formats, plus some new ones.