If you understood the airline industry, you would know that DEN is a bloodbath and a financial disaster for all 3 carriers. Averages fares in DEN are well below the US average for similar markets. F9 is hardly an example of a healthy carrier... it has been sold (or is in the process of being sold) and has lost enormous amounts of money trying to compete with WN and UA who are much bigger. WN started its buildup at DEN using its profits from fuel hedging but has still not "won the war" in DEN and DEN doesn't come close to performing financially for WN as other hubs are. WN execs have said so. UA is far from certain how they are going to win in DEN either. UA is now the 2nd largest domestic airline in DEN behind WN.
DEN is precisely the example of an airport that added enough capacity to accommodate plenty of airlines but that doesn't and hasn't meant that DEN is successful for any of them.
The same principle applies to NYC. Just because NYC is the largest market, has 3 airports, and hubs for 4 airlines, including AA, doesn't mean that they are all successful or all of those hubs will survive. It is highly doubtful that AA will become the dominant player in NYC that it once was or will be able to reverse its slide where it is now half the size of DL and UA. US brings very little to a merger because US lost a large portion of its NYC presence to other carriers years ago. US and AA have both lost so much market share and have dropped so many routes that even the combination of them is probably not going to be enough to make AA/US a viable airline in NYC. Since the other hub airlines also serve the same point to point markets that AA will try to maintain, it becomes harder and harder to envision new AA as being viable serving a handful of markets against other carriers that have much larger hubs.
You are absolutely right that AA's ability to compete long-term is heavily impacted by its ability to remain a viable carrier in NYC. It is precisely for this reason that US is looking for a merger because it pulled out of too many key industry markets.
WN is adding markets from a position of strength which is completely the opposite of what AA is doing - which is pulling out of key markets from a position if weakness. WN can afford to slowly add more presence in key markets and it will very certainly gain new slots to help build its presence in key markets like DCA and NYC but they aren't losing anything in the process and WN's core business is still fundamentally strong.
I'm sorry to rain on your parade but many of the key strategic challenges that AA has faced over the past 10 years have still not been resolved and won't be resolved with the US merger - and that is why so many people cast a leery eye at the merger in the first place. NYC and Asia are still significant issues that AA has not resolved and the DOJ could impose restrictions on the merger that could undo a lot of the benefit that AA/US have been expecting even though the long-term outlook for either carrier as a standalone are not great. That is precisely why they have been so vocal about being able to compete with DL and UA... but the key strategic issues such as NYC and Asia won't be resolved to the point that AA/US can compete effectively with DL and UA.