I love these BJJ philosophy type questions.
I think it depends how specific of weaknesses you are talking about. One should always be working toward well-roundedness and improving upon weaknesses, but you don't have to get too specific about them. For example, you need to always work on both your top game and your guard game, both your submissions and your escapes, and your takedowns, etc. You should be striving to make all those aspects of your game equally good, even if most people fail at it.
But you don't really have to think like "My weakness is this sweep from butterfly guard, I need to work on it" or "seoinage is my worst throw, I need to practice it" because there are so many techniques out there that vary in effectiveness for different personalities and body types that it's not possible or really even desirable, to be equally good at all of them. You need to be good at every position, but not every technique. You just need to have a couple of techniques that work for you, and can be chained together, from every position.