We say yes.
Let's look at the benefits:
Mindful eating. It starts with reviewing each meal as you record it. Eventually, it leads to thinking about each meal as you prepare it. And paying attention as you eat it. All things that make your eating more of a decision than a reaction.
Accuracy. Let's face it, you can't keep it all in your head. Drawing valid conclusions and recommendation from your eating habits and how they help or hinder your goals can't rely on memory or (ahem) gut feelings. That's a (ahem) recipe for disaster.
Aids your experiments. Finding out what works for you is a systematic process of trial and adjustment. You have to plan it and record it. You can't do this in your head or by winging it. Would you take a medication for which everyone involved in the clinical trial just relied on memory and anecdotes? Or would you want real evidence?
All in all, if you want results, you have to take a data-driven approach. That starts with collecting data. Once collected, data can be analyzed. Hypotheses can be formed and tested.
Obsessing over food (or anything) can become an unhealthy habit. But logging food and activity for a scientific analysis and a process of adaption is far from unhealthy. It's not an obsession. It's a method of getting sh*t done!
Don't go too crazy about calories. Think about servings. You will be looking for trends based on what foods you are eating at what time of day. Servings is refined enough.
No need to track time to the second. What's most important is what general time of day it is, morning, afternoon and so on. Break the day into four or five time periods.
Track activities too. When, what type (aerobic v. anaerobic), and reps or intensity are what matter here
Track sleep quality and quantity
Note down your intermittent fasting
Food logging can be as low tech as a journal and a pen. If you are interested in applying modern data analysis to your log, consider an application like MLog.