No doubt there are older people who use the phrase today, but that's still more annoying; they are the older people who are very proud of inserting 'cray cray' and 'yeet' into conversations.
'Flung' sounds better to me, but my original comment admittedly was performative. I don't really believe my word choices are objectively better than anyone else's.
It might be just a quirk with the corpus Google uses.
If it's not a quirk, then it is probably due to one usage of the words (eg: "So you got this angry customer, see?") peaking in the 1940s, and a different usage (eg: "You can do it... you got this!") rising in the 2000s.
I can't say who exactly is responsible for 'you got this'. It just began to grate at me the year when every new movie or tv show had a character saying it.
A similar phrase is 'I need you to', which appeared around the same time. Eg: 'Okay, I need you to calm down' or 'I really need you to be supportive right now', etc. To my ears it sounds gratingly self-entitled.
At least yeet can be funny if you're referencing a meme/being intentionally ironic. I'm not sure there's another great word to replace it anyhow, chuck or hurl are probably the closest but don't imply the level of reckless abandon, and aren't quite as "multi-purpose" in terms of understood contexts.