This is only true, if you do not value your free time. In your example, you've spent 4h to save 200$, so your work was worth 50$/hour. A freelancer with a 100$/hour rate might do 2 hours of work instead, spend the money, and gain 2 hours of free time.

There are other factors of course, but in general, many people come up with a rate for their own free time (which is often higher than the actual rate they charge clients)

It’s not only true if you don’t your free time. It’s only true if you’re a freelancer that is turning down hours at a higher rate than what you’re saving.

Many people working on products, both on their own and within a company, aren’t turning down other profitable work to optimize existing solutions.

If I watch a two hour movie instead of spending two hours saving $100/month, it doesn’t matter how much I value my time, no one is paying me $100/hour to watch a movie.

There's a difference between the initial example and watching a movie. That's what I summed up with "there are other factors (than money)". If I'm only interested in the _outcome_ and I treat the way to achieve it as work, I definitely weight the time cost vs benefit (and I am not a freelancer). If it is something I enjoy doing (which may or may not be true for the initial example), I'll take this into account as well. Time is a limited resource, and I treat it as such.