No, you don't need to develop your inferior function
It is common to describe personality development as developing your weaker functions. I think this stems from a misconception of how cognitive functions work and why we favour certain functions over others. INFJs favour introverted intuition due to the positive impact it has on an INFJs well being. Introverted intuition is one of the functions that can help an INFJ reach a state of flow and increased passion and motivation.
Inferior Functions Have A Grounding Role
As a function used by judging intuitives, introverted intuition is also about your sense of direction or how you reach your goal or passion. Think of it as how you travel forward in life. Now think about your opposing extraverted sensing function. Often, how people use extraverted sensing is as a "check-up" function. Okay, I did something with introverted intuition, now, what would happen if I retraced my steps with extraverted sensing? It is a little like drawing a line, and then drawing that same line again, to make sure your maths are right. Healthy exercise from time to time, but if you do it all the time, that can strongly halt your progress in drawing out your life.
The role of our inferior functions is to ground us and to make sure that we are not piloting off in the completely wrong direction. Often, what drives the use of our inferior functions is anxiety. Anxiety making us go "Hm, I hope I did that right.." and stress in the sense of making sure it was done thoroughly. This is also why often, our use of our inferior function appears to be filtered from our dominant function. It is used to check on our dominant function.
How Not To Look At Your Inferior Function
The unhealthy thing is to look at your inferior function antagonistically. Because we often experience these functions in times when we are more anxious or stressed out, often, we come to associate these functions with negative things. It is not uncommon for people to be in a state of rebellion against their inferior functions and anyone who represents them. This is silly for many reasons.
For one, our inferior functions represent real concerns we may have in our life in regards to work, chores, and things that we perceive as more tedious. Secondly, since you are mostly going to be using your inferior functions as an anchor... If you rebel against the anchor, it is not like you are going to stop feeling anxious or stressed. The problem will still be there, even if you try to avoid it.
The inferior function can actually provide temporary relief from worry and stress. It may not resolve the issue in itself. But it can show you that no matter how idealistic, wacky, or NF you get, you are still on track, and what you are doing still makes sense. Consider grounding yourself a weekly or monthly exercise, not enough to stop you from reaching your final destination, but enough to just make sure you are okay.
Should you develop your inferior function?
Some look at development as going from the dominant to the inferior function. For example grounding your NJ prediction with SP "reality-checks". But this is not the same as progress. Progress and development instead comes from grounding your NJ predictions against NP. While grounding is to check if your prediction was right, there is a problem. It only shows if it was right in hindsight, in reality. It doesn't show that you are right about the future. Often, the question of developing your inferior function is downright silly. Intuition is an INFJs passion, if you have a big passion, say to be an artist, why should you study to be an accountant? Unless, that is also your passion, in which case, wow.
Integration, which is a much more profound experience, is to not only find that you are able to predict the past or the present, but also the future. And what is the value of a prediction, if it can't predict the future? To grow, NJs, put yourself in the scary, intense situation of opening yourself to new patterns around you. Be in chaos, and in creative situations, and the world of different options. That way, you can write theories not just about the present, but also about the future.
You will for example find that NPs can release blocks you may have in your thinking. It is like firewood, as scary and uncontrolled as fire can be, and it can fuel tremendous growth in you. In short, SP feels annoying and tedious, but great when you are done with it. NP feels scary, but feels exhilerating when you have gone through with it.
So no, you don't need to develop your inferior function. You just need to accept that it is there, as your scared companion. It is your anchor, in times where you feel scared and unsure. What you need to do is develop your unconscious function. That's where true growth is.