Once you have this realization, what's the advantage of showing the proper error code to the user? Whatever it is, it's not in his power to fix it
While code fixes are not in their power to do, changing their behavior, or waiting for a better internet connection (i.e. "something went wrong" actually means "go log in to the hotel wifi") are things in their power.
Have you ever done end user support? Having a moderate amount of detail like an HTTP response code saves tons of time and headaches when a user calls in.
And some of the specific codes you mentioned (401, 403, and 429 for example) actually do give a power user actionable information. They can know that there's something wrong with their login credentials or permissions, or that they are making too many requests too quickly and need to slow down or wait to stop being rate limited. And knowing that it's some kind of 500 error lets a power user know "Ok, this probably isn't an issue on my end" which helps them stop worrying that it's something they're doing wrong or something wrong with their system.