I am giving an opinion about how I think this should work but I could be mistaken about what users want.

In the Pageview Analysis tool there is a feature to search for data in the range "last year".

If I use this feature, then I would prefer that it link to the last year at the time of my search, and not to call a new query every time the reader visits the graph. This would make the range persistent even in archiving.

Like for example, if I link to "last year" data in 2017 and intend 2016, then I would like for someone who views this in 2020 to also see the 2016 data, and not last year with respect to them meaning 2019.