I do my best. I have somewhat of an esports background despite not going professional with it just an enthusiast who's watched various competitive games. And I can understand your response to it.
Another way I did think of it though, but didn't use it as reference though was from other games with a team structure. Basically the Marvel vs Capcom series. Now even though you're not banning anything, the characters that get picked are all too repetitive now that there's an unchanging tier list.
Marvel vs Capcom 2; A 56 character roster and only about 8 are played mainstream these days on those rare occasions when it hosts tourneys.
Marvel vs Capcom 3: A bit more up to date, but harbors about 4 busted characters you either know how to play or play against it: Doctor Doom, Vergil, Zero, and Morrigan (honorable mention to Magneto). If a team had 3 of these 4 characters, it was probably not going to be fun or interesting unless he lost.
Now to string it back to League as a viewer perspective. You can see the same three bans or the same 3 picks per role and get bothered by it; I can easily relate that feeling of boredom to seeing the same 3 characters by a player in MvC. The standout difference comes from what you had mentioned: League is ever changing, not to mention time consuming. Fighting games back then never really had a shift in a character or even buffs/nerfs which recent fighters have started to do. Over time, a Champion's priority will shift based on what gets good and what goes bad.
I guess because of how I adapted to seeing the same fighting game over and over with MvC, I built a tolerance for seeing the same thing over and over for Mobas like League, Dota, and Smite, or strategies in shooters like Overwatch and CSGO, CSGO itself being a somewhat weak point of reference given its play as is.
But how do I keep up with it; what keeps me watching an expected degree of boredom? If I had to answer, particularly for fighting games where my esports viewing roots began, it would be from how insanely mechanical players had to be on a physical scale and that even one mistake or bad input could cost you and the crowd would just lose it.
That's about all I can say. Just adding a bit more depth on my response from earlier really. Change happens as the year passes.