And besides, that is very specific to web jobs. There's an awful lot more to the industry besides.
I can assure you that the bar for entry into my field is much higher than software. Like medicine and law, engineering requirements are strictly set by state law and professional boards. You need at minimum a bachelors in engineering to get a foot in the door. There is no self studying or civil engineering bootcamps. Afterwards, you need to become an engineer in training (EIT) by taking an entrance exam. Four years of experience later, you can sit for your professional engineers exam to become a licensed PE.
So now you're 8 years down the hole, finally licensed and ready to actually practice in a professional role. The kicker is that you're still probably making less than a fresh CS bachelors student working at <foo> corp in a tech hub.
I'll stick to posting on Reddit and contributing to projects.
There is no such trust in the education of software developers, perhaps because software development is such a new field. I've worked with great ones without a formal education and terrible ones that graduated from good schools. The way to 'prove' yourself to someone when they can't work with you (e.g. first stages of a hiring process) is to demonstrate your work by using technical articles, GitHub commits etc. Also, that stuff is not specific to web devs, I'm sure you can find every kind of project under the sun on GitHub.
Photographers, graphic designers and musicians.
EDIT: and, come to think of it, don't musicians need to practice for a long time before even getting a chance to perform for pay?
It perhaps depends on the specifics of the jobs you go for. For example, if you're a musician producing audio for eg film, then you definitely are expected to have a portfolio, but if you go out and play for an audience, then you probably don't.
Programming is similar. You hear the stories about how some tech founders focused their energy on programming, it took off and they dropped out of wherever.
I'd argue that for every one of those, there are scores of people who do it just for fun like they did, get nowhere but do it anyway because they like it. Just like there are scores of guitarists for your Clapton, Hendrix, etc.
Open source contributions to me look a lot like people, for the most part, enjoying themselves and getting better at a hobby.
Doctors have conferences, Chefs have "Chopped", and those are only the "mainstream" ways the general public knows about. Most others you mentioned have industry/trade magazines for example.
I suspect the other professions would benefit as well, it probably simply hasn't occurred to them yet. It reminds me of when I was watching a bodybuilding competition in the 80's and thought the posers could really use some advice from a professional dancer. Sure enough, this occurred to one of them, they did a routine that blew away the others, and then the rest of them did.
Is it good (for lawyers, accountants, etc.) or bad in your opinion?
It's true that the widespread expectation that a programmer will be programming (or doing related things) in his spare time is slightly unusual compared to other professions. Personally, however, I find that expectation natural and I would do it - write code in my spare time - anyway.