@Dodece
Unfortunately when it comes to Anime Popular and Available are synonymous in the West. The truth is that it really does taint the results. It isn't necessarily the case that a series is the best. Usually it is just the best of what little has been made available for sampling.
While it's true that the very limited distribution of anime in the West can limit our experience as consumers, this is now becoming a thing of the past with digital distribution, both official and unofficial (fansubs). And you clearly can't evaluate the experience of a person just by looking at their personal list of favorites. Besides, gaming has much better distribution than anime and yet, there's several games that constantly appear on all "best games of all time" lists. So there's always the chance that many of the favorites mentioned here would still appear, even with better distribution. In fact, if you take a look at what's popular in Japan, you can see that many anime mentioned here are also quite popular there...
Also, I believe it's worth noting that our opinion is always limited by our experience and will always be... And even those that have watched little anime or played few games could have experienced some of them that we haven't, which could be seen as holes in our experience in comparison.
Even if they were to only be attracted to Shonen Jump like fair.
This is besides your point, but I don't see how can you lump all Shonen Jump series like if they were the same. For example, Dragon Ball, I''s, Mazinger Z and City Hunter are all from Shonen Jump, yet they're completely different from each other.
When we were all four or five years old. We would all say that Sesame Street was one of the best television shows. For us it may seem true, but that is only the result of us not having a lot of experience which would allows us to develop our own unique taste.
Not the best example... Children are not capable of understanding many things, at least completely, due to being still in development from a biological point of view, not to mention their limited access to different media for a variety of reasons. Still, I do get your point and I agree that the more experience you have, the more you learn about your personal taste. Although let's keep in mind that our personal taste and views are always subject to change, not just by the things we watch, but also just by life itself.
Where I disagree is when you go from being a more "refined" experience to you to a more valuable opinion to everyone else.
Anyway it is a good thing to argue for people to try more series out. Rather then take what is handed to them it is only good for the medium. You can't really argue that it is a choice born out of knowledge. It is just a choice born out of slim pickings. You know we could always put this to the test by asking in the future for someone to provide a qualification for their choice by saying how many series they have watched.
As I said before, I completely agree with keeping an open mind and trying new things. But I completely disagree with the assumption that those who choose popular or shounen anime as their favorites must be ignorant, or that we should value people's opinion by how much anime/games/movies they have experienced. But of course, we're all free to choose the opinions we pay attention to anyway...
And what about the overall knowledge of said person ? What if someone knows a lot about anime but little about anything else ? Our whole cultural knowledge can also influence our judgment on the anime/games/music we consume, not just our experience on said medium. So why stopping on that ?
Should we provide a résumé every time we give an opinion on lists like these ?