It’s not just websites; search does not work anywhere. Not in email. Not for the local filesystem. Not in calendars or notes. And search is not all that hard, contrary to what you have been told. One developer alone writes a search tool that’s better than any other one I’ve used and works absolutely flawlessly. So it can be done.
For some reason, these companies just do not want to have working search. In most cases, I can’t even imagine why.