Is Firefox "reader" mode legal?
Is Google cache legal?
What about Internet Archive wayback machine archive?
Is deleting your cookies legal? How about spoofing your user-agent?
How about a browser plugin that automates what OP describes?
In the case of caches like Google, Internet Archive, or `archive.today` (same thing as `archive.ph`)... probably, in the USA? If it winds up in court, we will find out, eventually.
Simply reading anything on the web technically involves "making a copy" already, which is one reason it gets and has remained somewhat confusing and complex to determine what is or is not legal with regard to copying web content. You can't simply say "making a copy is not allowed".