I totally agree with you and I am on the convenience team. My father, however, is the crazy guy looking to save money. The thing is… he has a lot of money. For him, looking for bargains is a sport and the fun itself. Convenience, which you and I value so much, is not a thing for him. We have different priorities.
My behavior is quite similar to yours. I have a monthly budget but I am not picky about everything I do over the month, I just have an idea of where I stand as the month goes by to avoid bad surprises. It is fine to have outliers. The problem is the extremes of being over-controlling or of having no idea of your economic health at all. However, my 'budget' does not interfere with my big desires. If I hear a clear call from within to do a specific course, go to a specific trip/experience or whatever, I always hear it. I believe that whatever it is we deeply want will work out as long as we hear and follow. I don’t make big choices based on my budget: I make big choices based on my heart and then my body and mind make it happen. If we are based on our budgets, our life becomes constrained to a box. If we are based on our dreams, we are forever expanding the box.