The unintended side effect of this is that HR coaches you to be as vague as possible in responses. I can’t give real feedback because some feedback may seem dissimilar to other feedback and look like discrimination if you blur your eyes.
So everyone gets the same form letter.
Isn't the side effect also giving incentive to those companies to just not be honest in internal communication? But do the real conversation via call or different channel?
Unfortunately, many companies have chosen to comply with anti-discrimination laws by not giving any feedback. Nothing is less discriminatory than an empty string.
If you make such request, how can you enforce to get all of the comms? I'm curious, would some government institution step in and audit their mail servers, slack channels, google hangouts and all other channels to obtain all of the information?
The next stage of complaint is actually the local Information Commissioner.
Companies will usually comply with this, because it's very difficult to instruct staff to not comply with the law without leaving any records or risking one of them leaking it. However they will check what the legal minimum is and do that.
I take it you are unfamiliar with the legal process of "discovery" https://en.wikipedia.org/wiki/Discovery_(law)
Side effect of this is also to keep any bias out of the equation and, being on the other side, easier to call out colleagues making inappropriate or downright discriminating comments (which in my experience unfortunately happens everywhere still)