That's one way in which people sometimes choose a "right" or "zero" accent. Another is by social standing ("the queen's English" was literally that).
Either way, that's declaring one accent the right way of speaking, and describing people who speak differently as having a "heavy" accent instead of simply a different way of speaking.
Perhaps a specific example would make this clear. There are many dialects and accents of German in Germany. Which one would you declare the standard, and who would you describe as having a "heavy" accent?
My point is that making such a judgement is wrong to begin with, and one should simply describe a particular accent by its features or regional distribution, not as "heavy".
(And to respond, briefly, to the comment below: when learning a foreign language you choose to learn a particular dialect and accent. That doesn't make other accents "heavy", they just aren't the accent you've learned.)
In linguistics, this is the prescriptive vs descriptive debate. It's not controversial that a prescriptive grammar declares how a language should or ought to be used. Declaring one accent the standard is a similar prescriptive position.
Also, you are drawing the wrong conclusion. "Everyone has..." is simplistic. Some have more, some less is nuanced.