I tend to use two analogies to explain the importance of provenance in songs (other tradarts).
Archaeology is a good one to explain why we need to know who passed what to whom and when and how (oral, print, recording etc). That can be academic, but also visceral. Like bringing up an Elizabethan breastplate from 30 meteres and knowing we were the first to see it since the man wearing it went down with his ship. Some songs can give you that.
But perhaps an appreciation for antiques is more universal. You can admire the workmanship and materials of a Tudor chair, but the patina is also crucial, because it tells you about where that chair has been, and you think of who has sat in it, and how they lived. And it may be worth more than a Victorian carver with more wood, and more decoration. Some will like one, some the other - and others still will prefer the modern reproduction because its new, or even the Ikea one because they saw it on Property Ladder. But they all keep your arse off the floor.
So yes - singing them is vital, but always make sure you credit where it came from, so those who want or need to track back can do so.