"I'm going to the pub on Thursday" isn't likely to be archived and referenced at some future date.
Unless you Tweet it. In which case, your statement (and the relative, human-parsable time) and the timestamp (absolute, machine readable) are both present.
Repetition and redundancy can increase robustness and strength.
This would be a valid argument for not persisting dates as relative values.
It isn't an valid argument against presenting dates this way.
The OP's POV seems, to my eye, driven by the fact that primitive screen-scrapers can't just run a simple "toDate" function to provide it, API style, to some back-end. But it doesn't mean that it's not possible to convert them - it's not even that hard.
Fortunately, UI designers care more about their actual users than satisfying 3rd party leeches.
Unless you Tweet it. In which case, your statement (and the relative, human-parsable time) and the timestamp (absolute, machine readable) are both present.
Repetition and redundancy can increase robustness and strength.