There's no need to compromise an article to placate cranks on the Talk page; respond to them on the Talk page.  
There are separate questions:
Why is it called the "World Series"? 
Is it justifiable to call it "World Series"? 
Is "World Series" meant literally or just a label preserved for historic/traditional reasons?
Regarding the answers:
The answer would appear to be: 1880s hype + 120 years of tradition/inertia.  
The first bit should be in the history section. The reference says In 1884, the Providence Grays of the National League outplayed the New York Metropolitan Club of the American Association in a three game series for what was originally called "The Championship of the United States." Several newspapers penned the Grays as "World Champions" and the new title stuck. 
It would be nice to cite an 1884 newspaper saying something like "The Grays are now the Champions of the United States; indeed one might well call them the Champions of the World." 
"the new title stuck" is rather vague: did it stick instantly and unanimously? Looking at the contemporary match programs on baseball alamanac, 1911 is World's Championship Games, 1912 is World's Series, 1930 is for the Championship of the World, 1940 is World's Series, 1941 is World Series. It's worth distinguishing "World Series" the series of matches from "World Championship" the title at stake in the series.
The "New York World" urban myth is widespread enough to be mentioned and debunked. 
 "The title of this championship may seem odd to some readers" is not a justification for answering this question, since it relates to the previous question. The justification would be something like "Some people have (jocularly or otherwise) questioned the appropriateness or accuracy of the name World Series"  
I speculate that there should be some juicy examples of such questioning from U.S. journalists in the 1880s, or Latin Americans in the 1960s.  There is the quote attributed to John Cleese: "When we [the UK] hold a World Championship for a particular sport, we invite teams from other countries to play, as well."  
There are various arguments pro and contra that might be made. But only those that have actually been made by noteworthy sources should be given. 
The relevant information seems to be present in the article.