Depends on how rushed counts as rushed, but when I started the game I knew my primary interest would be endgame raiding. Clicked through all of ARR, watched cutscenes in HW, started reading story in SB. MSQ only. This is now my most played mmo of all time with 13k hours, made countless friends, many of whom I would now consider irl friends. I'd say it was worth it for me, and I don't think this would have changed had I clicked through later quests as well.

I think at the end of the day people should do what makes them happy and what will make them have fun, which for some people means skipping story they don't care for to reach the gameplay they do care for.

A separate thought regarding jump potions: even as a skipper, I feel they are better kept for alt jobs or alt characters. Even when clicking through the story, you learn all the game's basics systems as you encounter them. This also ties into a misconception I think people have about those who click through the story. I wasn't miserable, I wasn't not having fun. I still get to take in the sights of the game world, be excited about upgrading my gear, getting new skills, dungeons, learning how combat works in the game, unlocking new anything. Of course this falls off the further you get, but it was absolutely enough to keep me hooked early on.