I do not. I actually think it may be counterproductive in the early days of TRT because your body is changing very rapidly and it takes time for all those neuroendocrine changes to balance out. I seem to remember that I was at least 6 months into my program before I began to feel somewhat stable. For me anyway, Brain fog was lifted fairly early in my TRT program but the libido and ED thing took years to straighten out.
I see way to many guys posting questions and observations about how they feel after changing this or that, when in fact, what they are feeling may or may not be associated with the protocol or supplement changes they implemented. Our bodies often go through cycles of changes sometimes due to low grade infections, workout schedules, work schedules (stress), and other non controllable environmental influences. These can be short term (e.g., days), medium term (weeks), or even long-term (months). We have to factor those influences into how we feel too.
Even now, 8+ years into my TRT protocol, I am hesitant to draw any conclusions unless I have at least 8 weeks of the protocol change under my belt and appropriate labs (if there are any) for what I am attempting to observe. However, I can see the benefit of a daily log if you are dedicated enough to do it and regimented in your approach.