I don't think United will be hurt by WN's move. I remember in early 2000's, how the news channels kept reporting how United was the legacy carrier that was the most vulnerable to LCC's. And after going head on with WN, Virgin America, Alaska and JetBlue, United seems to be managing just fine. Lets not forget it was WN that just recently bailed from Newark. Also, United has had to deal with WN in Denver and SFO, their other 2 major hubs, and before the KaKa hit the fan, United was expanding gates in Denver.
When our plane went tech, United rebooked me on AA and got me home only 1 hour late. On another trip when our flight was running late and my connection to YYZ was in danger, the agent at the LAX United Club made couple of "Just in case" reservations on a later Air Canada flight. Oh and being able to get to Kansas City, Ashville NC, Zurich CH etc. all on one airline / one alliance is highly valuable to me.
On United, I can same day change and same day standby especially now without any change fees, changing flights is even easier. On United, even basic economy can do standby for free. On WN, you can't make any changes if you buy their cheapest fare including standby for a different flight.
The last 2 times I flew WN, both flights were 5+ hours late. Lets just say everyone in my group was asking me if we could access the United Club which we could not since we were cheating on United with WN. Oh and don't get me started on WN's early bird check-in fee ($15 - $25 each way) which doesn't even guarantee you a spot in Group A.