This is a good direction, though to be warned that it will not be trivial. The key reason why page needs a pointer to page_set is because the mapping from page to wpr recording is stored in page_set object (https://cs.chromium.org/chromium/src/third_party/catapult/telemetry/telemetry/story/story_set.py?rcl=ee85992c5c619df6e291ba6dc2e86654f344a492&l=24)

Could we just move it to not be in the initializer? I guess that would have the issue of if someone added a single page object to multiple page sets then we would end up with the single page instance having only a reference to the pageset that it was most recently added to. :( 

Note for posterity that this idea was inspired by the hoops that I needed to jump through for https://chromium-review.googlesource.com/c/chromium/src/+/1356320

When I looked at this problem back then, the fix I come up with is to remove the need of the map from page to wpr recording. Instead, every page instance must specify the location of their wpr record.

That solution makes sense to me.