It's an area ripe for study. Certainly collectors in Victorian times (as opposed to mere "putters away" of new types) didn't really bother with their own base metal coinage, and the rarity of BU bun pennies possibly bears this out.
Had that changed by 1913? Very difficult to say, but it may be that "putters away" of 1913 pennies accounted for the survival of now rare varieties in high grade, the circulated examples of which were swept up in 1971.
I absolutely agree with the case of people putting away examples of new reigns when they first appeared, which helps explain why the 1902LT penny is relatively easy to find in top grades, it being the earlier variety and therefore the first to appear.