(1) In broad general "graphical design" terms -- don't do this. It looks like total rubbish. The "reason" is that you want consistency to imply distinctions and tidyness - the whole reason that different elements or concepts in graphic design will be consistent (whether color, size, typeface, etc). So, any "graphical designer" would just say "don't do that, it looks stupid" and that's correct.
(2) That being said, there is a look where if you have REALLY ENORMOUS headlines, you can equal them out like this. You could say, all the headlines are so enormous that it is perfectly clear - compared to the body copy - that all those "enormous" headlines are the same thing, even though the fount size is different.
(Interestingly, this can be either a sort of "Victoriana" look (rather like an exciting! ad from boy's-own magazine or a railway timetable or the like) or indeed a modern hip sort of thing (there was a magazine from The Face period that would always annoyingly do this, I can't remember which).)
I think, but I'm not sure, this is sometimes called a "stacked" headline look.
For an example go HERE and look at the Gorilla Coffee example (red background).
(There are endless examples of that "stacked" headline look in advertising etc lately - I just found it tricky to google them up! I'm sure others will offer any number of common examples from current brands.)
To reiterate, if you're simply asking "should I do this for headlines in my long-form article" the dead-simple answer is (see "1" above), don't do it, it looks silly.
But I'm just bringing to your attention that this "stacked headline" look does appear, more in sort of bold posters, that type of thing.
Finally, (3)
It is perhaps of interest to this question that:
shrinking font sizes for headline-like elements (or whatever) are a built-in feature in iOS (for many years now).
(Purely for the interest of anyone who doesn't program for iOS, here's an example: you can see it is nominally Helvetica 11. However I turned on "Autoshrink" and if the name gets long it will shrink it to in this case 6 point as the worst-case. Beyond that it will just cut off the text.
)
So, in apps, this is indeed standard behaviour, and, you'd pretty much always use it in the case where the text is generated dynamically, i.e. you don't know how long the title of the chapter, street addrees, here a person's name, or whatever, is going to be. (I guess the only alternative to autoshrink, if the dynamic text turns out to be too long, is just trimming the text - you have to do something, you can't just make the app crash.)
So it's worth considering that (for better or worse) this happens by default, in iOS apps - basically any business or text-based (non-game) iOS app.
(Really, in apps, I think it sucks ... but again there's really no alternative, if the text is generated on the fly and it has to fit in some space - other than just leaving it out or trimming it.)
So, it's conceivably that "young people today," non-UX-professionals, looking at your question here, would just say "What, of course do that, it happens everywhere" ("everywhere" meaning for them "in apps").