Sure working on your weaknesses makes sense at some level but since we only have so much time why not start by optimizing your strengths first and then if you have time work on your weaknesses. The truth of the matter is you should not ignore your weaker areas but identify and acknowledge them. Learn
you limitations and figure out how to leverage your strengths against them or to work around them. You can’t do everything so why wouldn’t you do what you are good at and enjoy and outsource the rest? When you hire an employee don’t you look for someone who is particularly good at the tasks in that position? You don’t hire someone that is not good at that job and try to make them good at it, you hire someone that has at least good performance in that specialty and that enjoys it. That way the natural tendency will be to grow in the area easily and naturally.
A strength is not and area you are necessarily proficient at currently but a strength is an activity that invigorates you and makes you feels strong, passionate. Because of this you instinctively look forward to it, you get lost in it, time seems to stop and you get lost in the moment. You feel connected and authentic. Because of this it naturally has your focus and attention and you become good at it, not because of innate talent but from the practice and rehearsal that area gets subconsciously.
Conversely a weakness is not an area you are not capable of doing well, its an area you have not focused on do to a lack of interest and motivation.
This ties in to time management as well. We have a tendency to do what we like and are energized by things we are passionate about. Thus when we can work in these areas we seem to be so productive and get so much more accomplished and the fact is we do! So knowing your strengths helps you to be more productive and get more things done and they are thing you like and are good at. Do you see how someone that plays to their strengths can achieve a much higher level of performance than someone who is spending time trying to get better in their week areas?
Its hard to let go but remember you only have so many hours in a day, days in a week, weeks in a year and years in your life! So at least start with the things you love and are good at and if there is time left then you can cut the grass!