Iff your writing style is well aligned with the SA model. Sentiment analysis has always been a bit dodgy for individuals, but it mostly works due to sheer numbers.

Sarcasm, for example, works very poorly with SA, and if you tend to write sarcastic prose, SA will be a waste of time at best, and counter productive at worst.

He said he'd take a subjective measure - a journal - and take objective measurements of that subjective measure.

I would say that's still a subjective measure; it sounds like you disagree?

I would disagree.

“I love these chips” is subjective. Rate-of-saying “I love (.)!” is objective.

The absolute rate may or may not be important (I’d guess low importance), but changes* to the rate can indicate that a life changing event had a much larger impact than one may be subjectively conscious of, especially if the change was gradual — a loved one becoming gradually more ill or more emotionally distant, for example, slowly enough that one does not realise that light and joy has begun to leave one’s life until after the recycling bin overflows with beer bottles.

If I'm trying to make myself happier, and I measure how many times I tweet smiling emojis vs frowning emojis, I can simply stop tweeting frowning emojis. Thus the metric is improved without any change in the underlying thing being measured.

An objective measure, like weight or hours of sleep or time to run 5km doesn't have this property.

It’s possible to cheat, but (1) why bother? You’d only be cheating yourself; (2) how do you know to cheat if depression has snuck up behind you, and that sneaking is what you want to be automatically alerted to because depression doesn’t tell you it’s depression it tells you that you suck and it’s all your fault and you deserve it.