No? Because what would it be based on and if you edited the thing that it's based on then the URL would either change, or get out of sync which woudl suck. You could ignore the suffix meaning flickr.com/mwichary/sets/72177720330077904-<everything-past-the-previous-dash-is-ignored> I'm not sure if that would be a positive, although I guess S.O. does something like that. The issue is other sites really want to know if it's a link to the same resource or a different resource. And while you could redirect to the new one that just makes more work for everyone.
> I would get rid of /photos
I wouldn't because then you'd had have https://flickr.com/settings but that would not be a user named "settings" and the same for every other alternate purpose URL