I put the question to Bard AI seeking an Oxford dictionary interpretation and got this response.
"Both "America's Got Talent" and "America Has Talent" are grammatically correct. The Oxford English Dictionary defines "got" as both a past participle of "get" and a contraction of "have got". In the case of "America's Got Talent", the "got" is being used as a past participle, meaning that America has acquired talent.
However, the title could also be interpreted as using "got" as a contraction of "have got". In this interpretation, the title would be saying that America possesses talent.
The two titles have slightly different meanings, but they are both grammatically correct. The title that was chosen for the TV show is likely more catchy and memorable, and it also leaves open the possibility that new talent will be discovered on the show.
In American English, it is more common to use "got" as a contraction of "have got". In British English, it is more common to use "got" as a past participle.
Ultimately, the correct way to write the title is a matter of style and preference."