Look whether you want to look at analytics or not they still exist not unlike the laws of physics. You don't have to understand how gravity works for it to have an impact on you.
Perfect example is that Pop just isn't that into analytics but it doesn't matter because he's a basketball genius who intuitively understands the game and he instinctively builds and runs his team in a way that analytics will favor. Other recent champions (Celtics, Heat, Warriors) all relied heavily on analytics to help build and run their teams. If you rely on analytics to the exclusion of everything else of course you won't reach the ultimate level of succes, but which team would you rather have - Houston, Lakers or Knicks? At least analytics can help establish a floor of competitiveness.
I don't really think fantasy sports bears any relation to analytics by the way, they are actually more in conflict than similar. Counting stats are great for fantasy but tell you little about how effective a player is without context. My good friend who is big in analytics (ESPN includes him in their expert panel voting) doesn't play fantasy sports nor do most of the guys he tells me about, although since many work in the league I guess that could be part of it.
Which team I would rather have depends on whether I'm an owner or a fan, to a certain extent. While winning and marketability are related, they're not conterminous.
And "stats vs. analytics" is something of a false dichotomy. Analytics is all about stats. It's just a question of which statistics most effectively convey the information you personally deem important.