The esport fans I know have nearly zero overlap with the traditional sports fans. I don't think either is currently worried about losing their audience to the other.
I'm a huge sports fan and League of Legends eSports fan, and I try to watch Overwatch Legaue but just don't think the game itself is fun to watch. I don't think there are lots of people like me, but we do exist!
For me, I actually wish esports were more like traditional sports when it comes to game changes, rather than the other way around. There's no chance for truly deep strategies and specializations to develop when the rules are changed every couple months.
The problem with esports is that they can't often stay extremely static.
They tend to be much more unbalanced than traditional sports. If a "cheese" is found, then the game quickly becomes all about microsecond timing at pulling that strategy off, and no real innovation or change, which at least to me is boring to watch.
That being said, there are esports games that don't really "change" all that much or at all. Games like super-smash-bros melee or super Street fighter ii come to mind, where the "rules" have been fairly stable for a while now.
I would suggest looking into Counter Strike as an eSport then... the esports scene for CS has been around since early 2000's and has a rich history of strategy as well as skill. The changes that Valve make to the game are always in respect to the professional game play and always cater to the high skilled arena.
keep in mind that esports are still quite young. the top three games right now seem to be csgo, LoL, and dota 2. none of these games have lineages that go back more than twenty years. my guess is that the first twenty years of what became baseball, soccer, etc were even more unstable in their rulesets.
i think your take is correct in the long run, but developers have a long road ahead of them before they are creating truly balanced games that can endure decades without change.
What do the data on this look like? Anecdotally, I know lots of sports fans and very few e-sports fans.