So your NAS idea is probably the best with the caveat at your need to upgrade it regularly as well.
Compare it to a floppy disc from your grandparents. Not that bad for 3,5"? How about 5,25"? No? Then 8". These are now hard to come by. And this is just in the time span of 30-50 years.
The best bulk storage format was actually available early on and very shelf stable if treated reasonably: Paper tape. Low density and readers are hard to come by today.
Your primary point that our grandkids won't care is on point. We would drown if we keep everything. But the counter point would be that if we do not even try to preserve anything we would probably end up with nothing.
But for every average Joe who does not care we seem to have plenty data hoarders to make up for that.