I think for many people they do pick a game in the series they grew up with, and they cherish it. It seems especially true for Zelda. It's a shame GameCube titles are so isolated. You can buy many PS1 and PS2 games on the PS4 shop, but for the most part if you want to play a GameCube title without emulating, you have to actually have the console, or have a disc and a backwards compatible Wii. I hope they add a few GameCube games for the Switch shop, particularly Wind Waker and Mario Kart: Double Dash. I've only played very little of the latter. When they put old games on new systems, it gives an entire new generation the chance to grow up and be fond of that game. I wouldn't have gotten to play Ocarina of Time because I was born after the N64 era, but the release on Virtual Console allowed me to grow up with it.
And it's a valid point you made. I think outside circumstances can effect your outlook when playing. For the same reason I couldn't fully get into Wind Waker when I had the chance. But loved Majora's Mask.