I'm really surprised this idea hasn't been suggested by anyone. May be it has...
This could be a great feature for those, who travels a lot and as a result of another trip to another country may want to share which routes they've covered in this country.
This is the most desirable feature for me in Strava.
I know in FAQ there is a suggestion to use a screenshot of the personal heat map. But this workaround looks a bit lame. And I can't see the reason for not having this feature officially. It can't be privacy issue, because if I share it, it means I agree to reveal my personal data.