One of the reasons people find DOTA-likes so unlikeable is the incredibly steep learning curve. It is often said that you know nothing about LoL or DOTA until you've played 1000 games. At around 45 minutes a pop, that means you've got to commit way more time than most people have available in order to get good.
The games are more like basketball than Quake. 5 on 5, and if 1 player on a team is bad, that team will probably lose. It's why the communities in MOBAs can be so toxic.
Of course, real life sports take tons of practice too before you can have much fun. A total beginner can't just pick up a tennis racquet or basketball and start volleying or shooting hoops.
Making a game/sport that is rewarding at the pro level and also has no learning curve- does such a game even exist, electronic or not?
To be a top notch player, yes. Honestly my brother & I were having a lot of fun the first night we played LoL. Now going back and showing someone new is painful because you realize how much knowledge was accumulated over the years. But either way, it can still be fun.
I have about 3000 hours in Dota/Dota2 combined, I still refuse to play certain heroes because I don't know how to play them effectively yet(Invoker comes to mind). The learning curve for the base game is very high, then you have to consider that each hero is unique and has their own learning curve and when you have 100+ heroes it's very difficult to master.
The worst part is that even if you only like a few heroes, you at least need to be aware of every heroes capabilities or you will not do very well. If you don't know what every hero does you can't be sure that it's safe to engage in a fight.
In Quake you can also have 5v5, e.g. in Team Deathmatch or Capture the Flag. While it's not as much based on tactics, it sure feels a lot closer to basketball in terms of speed, and one superior player can carry a whole team.
And with movement based mods like CPM, Defrag or WSW, the learning curve is also kinda high, with 10 different weapons (ok, 3 major ones) and a movement system that is very involved with the maps.
It's steep if you can consider a tall cliff steep.
Warcraft 3 has a steep learning curve, like RTS games do in general. One mistake can cost you your hero, which can cost you your hero if the death is untimely. (I guess DotA derivatives are more forgiving in that sense.) But there aren't that many units and heroes to learn, so at least after some time you won't be taken completely aback when your hero gets ensnared, critical striked (struck?) hexed and then critical striked again. I mean, it will happen, but the possibility would have already crossed your mind.
There is a ton of finesse and micro to playing a game like WC3, but learning to play the game isn't that hard; there isn't terribly much that you need to memorize, and then you can concentrate on strategy and mechanics. DotA (derivatives), on the other hand, is built in such a way as to be absolutely relentless towards anyone who isn't already experienced.
WC3 is hard to learn, but not unreasonably so for an RTS. It also has a high skill ceiling. DotA (derivatives) are really hard to learn (I won't comment on the skill ceiling, since I don't know). Yet, people - casual players included - have embraced DotA over the humble original game. I just don't understand the attraction, particularly when it comes to the more casual players.
To be any good at WC3, you need major micromanagement skills: Blizzard games are what brought us concepts like actions per second after all. It's a bit easier in that respect than Starcraft, but still, it's really about multitasking and micromanagement.
You need a lot of knowledge to play Dota well, but you do not need that micromanagement: Pick a simple hero, like Wraith King, and you control a single character with a single active ability. Even top pros take less actions per second than an average warcraft player.
This difference in skills means that it's much easier to notice your own progress in DotA than in WC3. I watch a top DotA player, and I can see how I can get to be that good. If I look at a top RTS player, I realize I could not get that good if I spent a hundred years training.
The games are more like basketball than Quake. 5 on 5, and if 1 player on a team is bad, that team will probably lose. It's why the communities in MOBAs can be so toxic.