1. Vince McMahon still stands tall

Throughout its history, WCW had had quite a few creative and business heads, including its late stages when people like Eric Bischoff, Vince Russo, and Kevin Nash were power brokers. Even if WCW had defeated WWE in the Monday Night War, there’s little reason to think they’d stabilize for long. On the contrary, they’d go looking for another person to head up the company until someone truly stuck (or, more likely, until the company still closed down).
While he was WCW’s arch-rival, it’s hard to imagine anyone with a better overall booking track record than Vince McMahon, at least in terms of longevity and moments of explosive success. It’s reasonable to think he would have ended up working for WCW at some point had he lost the war.
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Alternatively, after WCW shut down anyway, McMahon would have been a prime candidate to rise from the ashes with a new wrestling promotion. While WWE winning lent McMahon the greatest consolidated power and resources, even if his company had lost, it’s realistic to think McMahon would have found his way back to the top.