If we track "hours worked" only, that metric might be of little use toward productivity.

Depends on the given person's level. Where I am now, the main problem is completely avoiding the work, instead wasting all my time online. If I succeed to put at least 1 hour of work towards my goals every day, then I am ready for the next lesson, which is making this hour more efficient.

Meta: Perhaps we could start by describing various levels of goal-reaching-inefficiency, creating a self-diagnostic questionnaire, and then give specific advice for each level. Something like:
Level 0 = you are not even able to log whether you work or not. Advice: unknown.
Level 1 = you are not working. Advice: use Pomodoro.
Level 2 = you are working only on low-priority stuff. Advice: prioritize.
Level 3 = you are working on short-term high-priority stuff, but you don't have a strategy for increasing your skills. Advice: set apart some time for long-term improvement. Etc.