dota isn't designed to appeal to newcomers. so "unintuitive" stuff like denying, multiple shops, damage types and so on doesn't matter. it's assumed that the player already has hundreds of hours played and at that point the "obtuseness" is irrelevant since players learn along the way anyway. New players are often brought in and trained by friends so the steep learning curve doesn't really matter. For myself and the people I've brought in, we've all found the experience of learning and figuring stuff out from the beginning rewarding and fun. People who come from other mobas usually feel that the game is wrong, and have a hard time adjusting, this is obviously also true for dota people who try league.
I wouldn't attribute lols success to gameplay or streamlining. It matters to some small degree but it's 90% timing and the fact that moba players really hate switching games.
LoL was one of the first big f2p games and at the time it came out there was no other free modern moba experience available. HoN was pretty good but the price tag sealed its fate. When dota 2 came out lol was already pretty huge and those players were never gonna switch.
I do however think that valves strategy for china and korea failed(which is how big % of LoLs userbase?). From what I understand steam has no presence there and so valve had to outsource administration of the game servers and infrastructure to perfect world and nexon. this happened too late and was too much of a half assed effort. for example it's a much more annoying and troublesome procedure to acquire a dota account than lol in these countries.
So anyway, I think lol could have been identical to dota in terms of mechanics and still had the same success because their popularity was based on timing and business advantages in the Chinese market.
Personally I prefer dota 2. All the mechanics and gameplay aside, in dota every hero is truly unique in terms of what it does. There is almost no redundancy and no real substitute for any given hero. lol has more champions because that's how they make money, they are incentivized to release heroes even if it doesn't help the game. in dota they'd need a unique design which is hard enough to come up with after more than 100 released heroes and even then there so much that can be done with existing heroes in terms in terms of balancing and redesigns that there really isn't much of a need for more stuff.
Additionally in terms of software engineering and the game client/infrastructure, valve is so far ahead of the competition that it's not even funny. it's 2016 and LoL still doesn't have replays? how is that acceptable?
It's not fundamentally flawed, the vast majority of champions can be played at anything below the pro scene and be viable. A lot of it is based on the meta with League so while the champion pool at any specific time may only include 60% of the champions, the actual champions in that pool will often change. Not to mention, just looking at the champions that are played at the highest level isn't the only way to judge how balanced they are.
League of Legends
highest win rate in ranked: 55.4%
lowest win rate in ranked: 44.5%
Dota 2
highest win rate in ranked: 60.47%
lowest win rate in ranked: 35.27%
dota 2 is balanced around competitive play not pub games, so those numbers don't matter much.
For example earth spirit has a 42% win rate in pubs, io 34%. #1 at 60% is omni which is never seen in competitive play.
Player skill and team play matters enormously in terms of what heroes are viable.