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I agree that this is a bad idea.
1. Cookies are generally a nuisance. I like the fact that docs.python.org is (apparently) cookie free and that python sites only use a few short-lived cookies. The complications you propose would be a nuisance to create and maintain.
2. Not too long ago, we created docs.python.org/2/ and /3/ so people can use generic links to the latest docs for the latest released version of either Python 2 or 3. The aim was to reduce the problem of links to stale docs. Both sets of docs have version added notes for changes within a series. Those two docs are not interchangeable and should not be automatically switched.
If someone links now to a fixed version of the docs, they are either ignorant of the new system *or* they have a purpose that should not be over-riden.
If someone quotes or paraphrases a portion of a page (which is a claim about what the page says) or otherwise makes a claim about Python, and posts a link as evidence of the claim, clicking the link should take one to the 'evidence', not one's preferred version.