"Is it so implausible that pilgrims then, as now, would want a memento of their visit to take home with them?"
No-one could call it implausible I guess, and I'm a big fan of speculation based upon an initial hypothesis that the ancient people may have thought and acted just like us.
On the other hand, I find it a bit disturbing to think that thousands of years ago, on the very site of EH's visitor centre, there may have been stalls selling over-priced commemorative tat!