There are incomplete parsers that cover most of the Org basics. For example, GitHub has one, crafted in Ruby. They use it to render e.g. readme.org files in repositories. It works quite well. I find the Org format very pleasant to work with.

I think the trick with Emacs and Org is to stick to the basics and then only add features or change your configuration very slowly, as needed. I have been using Emacs non-stop for >20 years and my .emacs is just 20 LOC. It's been shrinking, not growing. My goal is to bring it down towards 0 LOC. I have committed a few things upstream to modernize defaults.

Personally, I think the reputation of Org, Emacs, or Nix being hard and complex is undeserved. It's rather a documentation problem. There's no simple documentation to onboard newcomers and show them the basics in a principled way. So it looks like a mess, but it isn't.

This is incorrect. You can write a parser for org. See for example https://github.com/tgbugs/laundry. Work toward standardization has been stalled because I (among others) have not had time to circle back to work on it. In part this is because the lack of a standard has not blocked most use cases since emacs is open source and can run almost anywhere.

Why can't a parser be written? Is there a halting problem or a grammar conflict? Or is "can't" short-hand for "too much trouble"?

I also don't use org-mode anymore, but sometimes I really do miss org-babel-tangle. In contexts where doctests aren't available it can be really helpful for making sure code listings actually work.