Technically it does that, yes. Rarely do I see people taking advantage of it, though; most of the times I tried to copy some text out of PDF, the result had to undergo a significant cleanup before becoming usable.
It really is a problem with PDF that it's too easy to get a file where copy and paste yields a different result than what's displayed. But this varies widely with the software used for creating the file (e.g. latex ligatures never work in copy-paste)
When people write text and data and tables on the computer then put it on a paper-like format to share that's when the problem happens.
If you designed a real bad format on purpose, it would be hard to top PDF. Maybe Photoshop files are worse.
This should output a single file and ideally it should have some way of ensuring the author it won't be modified unnoticed (that's one of the features common people use PDF for, today, they think it is something no one can modify) -- perhaps signing it with a key from Keybase would work in the mid term.
https://github.com/iffy/lhtml has something going in this direction.
Sure, PDF is a light on context clues for automation and is targeted purely at humans. But formats targeted at both computers and humans consistently fail (XML with accompanying XSLT comes to mind), and/or only have terrible tools for creating files (easily parsable, pretty HTML).
Either there is very little real demand or we consistently fail at making alternatives viable.