Why not hire part-time developers?

I think your basic premise might not be correct. If you only are getting 4 productive hours of work done per day, then something is wrong. I would say you probably only get 4 productive hours of WRITING CODE (maybe much less), but during that long lunch break, or bike ride, or whatever, you are probably thinking about the problem (consciously or not).

If you work part time on two different projects, you simply won't be as productive, because you won't have that "down time" to think about problems.

I don't really feel the difference between planning/coding. It's all the same to me in terms of problem solving.

Also, I already do this as a consultant, and clients are usually mostly focused on speed and quality. So I give them 4 hours a day, I take a couple hours off then I plug away at my own projects for a few more hours.

The context switch plus the long break makes it work for me, but everyone is different.

Depending on the project, thinking about solutions during down-time does make sense - but no employer I've ever come across sees it as productive anyway. There's always the silent expectation to look like you're actively working. In any case, I'm often thinking about my work during the day regardless of whether I'm on the clock or not so this is a moot issue for me.

What amount of time are you billing for, and how do you track it?

What the hell is investigating a design?

Also, no company I've worked for ever bothered with proper documentation, and I've never seen anyone lower than tech lead ever do any of those kinds of things more than once or twice a month (besides meetings).

I'll concede these kinds of responsibilities might be more common in larger companies or different fields, but I'm thinking more about smaller startups.

I experienced this in the extreme recently. I'm a very experienced dev in a very in-demand field. Money is not a huge priority for me in my career. Flexibility is. I have a proven track record of success in part-time roles after converting to part time at my previous company (after 2 years of full-time, of course). I spent 3+ months trying to get part-time engagements, and was willing to consider both consulting and W-2 arrangements. I got interviewed and then ghosted by two companies, was offered a laughably low rate by a third, and a fourth showed interest but then basically told me that I'd need to work a 40-hour week. I know that a vocal minority has success in part-time consulting, but it's quite difficult to accomplish if you live outside of a tech hub (I'm based in Central Oregon) and don't have SV connections.

Contrast that with when I gave up and decided to make myself available for full-time (remote) work. In the span of about 5 weeks, I got over 200 recruiter emails, interviewed at 10 companies, and received 10 offers, mostly in the upper end of the $200k-400k range.

I firmly believe that this is a cultural block, rather than one that's rooted in rational/pragmatic concerns. Tech companies want to feel like they're getting your full intellectual output, even if that's demonstrably false in the status quo. There's also this issue that gets brought up of "if Bob is gone half the time, isn't that going to breed resentment with his full-time coworkers?" (answer: only if you have a shitty "butts in seats" management culture).

I honestly don't think we're going to see meaningful change in this area for a while. The 40-hour work week is something that's heavily ingrained in tech culture, to the point where certain companies' "perks" are heavily tuned towards incentivizing you to stay at the office longer and frequently turn that 40 hours into 60. I think it will take an external disruptive event on the scale of COVID-19 in order to change this aspect of tech culture.