Was I wrong about any of the four I named?
Tom Seaver as the best player in Mets history is pretty hard to argue against, same for Randy Johnson with the Diamondbacks. You could double the career of any other players in Twins/Senators history and Walter Johnson would still come out on top there, so unless you want to limit things to only the Minnesota portion of that franchise (which I don't), The Big Train is an even easier choice than Tom Seaver or Randy Johnson.
The only debatable choice from among the four I chose is Bob Feller as the top player in Indians history, and it's an interesting debate. If you go by the numbers each player actually accrued with the team in question (which is the general idea here), Nap Lajoie and Tris Speaker each probably merit being placed ahead of Feller.
Feller was on his way to sign a new contract with the Indians in December of 1941, when he learned of the attack on Pearl Harbor. He decided to enlist in the Navy, and missed almost four full seasons. During the couple years before that, he'd averaged ~9 WAR a season. If you prorate the portion of 1945 that he appeared in after returning from his military service, he was worth ~9 WAR a season again in his first couple years after being away. I don't think we can just hand him that value, but if you give Feller even half that credit, it's enough to move him ahead of Lajoie and Speaker. (Let's Go Tribe agrees with me.)
I stand by my initial choices; the Mets, Diamondbacks, Twins/Senators, and Indians each have a pitcher who deserves the title of "Greatest Player in Franchise History."
Of course, checking to see whether I was wrong about any of the teams I named is only part of the work to be done, because it's entirely possible I missed someone (or multiple someones).
Are there any teams I missed?
In the National League I don't think I missed anyone, though there are two teams you could argue for:
The Dodgers are one of the oldest and most storied franchises in American sports, but they're collection of greatest players isn't quite as impressive as it seems like it should be. Much of this is due to probably the two most storied players in franchise history each having had a relatively brief career. At FanGraphs, Duke Snider, Zack Wheat, Pee Wee Reese, Jackie Robinson, Don Sutton, Don Drysdale, Dazzy Vance, and Sandy Koufax are all within 10 WAR of one another, and Sutton is actually on top. Reese comes out ahead in Baseball-Reference's version of WAR, while Vance is at the top in WAA (Wins Above Average). In a better world, Jackie Robinson would have been in the league at least three years sooner; similar to giving Feller credit for time missed due to WWII, I'm spotting Robinson some credit for time missed due to systemic racism.
The Marlins have won two World Series in their 23 seasons of existence, but whomever their best player ever is, it's a less impressive guy than any of MLB's 29 other teams have. Baseball-Reference has Josh Johnson with the highest WAA (Wins Above Average) of any player in franchise history, but only by a little, and he's behind both Hanley Ramirez and Giancarlo Stanton in B-R's version of WAR, and he's even farther behind them both at FanGraphs. I'd go with Ramirez for now and probably Stanton in another year.
In the American League...
The A's don't have a standout player, because most of their greats spent much of their career with another team. For me, Rickey Henderson wins out, a short distance ahead of Jimmie Foxx. Pitchers Eddie Plank and Lefty Grove are each guys one could make a case for, if so inclined.
There are two teams I whiffed on though...
The Angels may be a year away from having Mike Trout take over as the greatest player in franchise history. (Mike Trout is only 24 years old, by the way.) For at least a few more months though, the title ought still belong to someone else: Chuck Finley. Your initial reaction might be that Chuck Finley can't possibly be the best player ever for a franchise that has been around for 55 seasons, but it's been a strange 55 seasons in Los Angeles, California, Anaheim, and Los Angeles of Anaheim. Finley leads all Angels in innings pitched, and his context-adjusted ERA (ERA+) is as good or better than everyone else who's pitched even half as any innings for the team. He leads all Angels in both versions of WAR. I'm surprised too, but Finley is the player Trout will pass.
Finally, the Blue Jays. I'm not certain who I had in mind as the team's best player ever. Tony Fernandez, Carlos Delgado, and Jose Bautista's numbers with Toronto put them pretty close together, and while I probably wasn't ready to commit to any of them, I'm sure I figured one of them was the rightful owner. I was wrong though. Not only are none of those guys the best Blue Jay ever, none of them is the second-best either. Pretty clearly, Dave Stieb and Roy Halladay are the franchises top two players... or maybe it's Roy Halladay and Dave Stieb. During his final eight years with Toronto, (2002-2009) Halladay was arguably the best pitcher in baseball, so I'm not sure why I overlooked him. Stieb, on the other hand, is overlooked all the time. He was the best pitcher of the 1980s though, and while that has a lot to do with better pitchers starting or ending their careers during the 80s, leaving few whose prime is captured entirely by that decade, he doesn't get nearly the attention he deserves. Allow me to do my small part towards correcting that by naming him the best player in Blue Jays history.
By my more careful counting, the greatest player ever for 6 of MLB's 30 franchises were pitchers:
Angels: Chuck Finley
Blue Jays: Dave Stieb
Diamondbacks: Randy Johnson
Indians: Bob Feller
Mets: Tom Seaver
Twins/Senators: Walter Johnson