Actually, there kind of is a reason that League can't seem to attain DotA 2 levels of balance (which some people would claim isn't that good, but I'm with you on that point).
DotA 2 as a game was launched from beta with a much more developed perspective of what MOBA is and how to do it right. They also had the entirety of LoL, the original DotA, and every other MOBA before them to perfect their formula off of. Now, Dota 2 doesn't have perfect balance (no game with constant DLC will be) but what makes theres better since its initial launch is that they patch the game much, much more frequently on a smaller scale allowing for faster output of material that course corrects the game more frequently. That kind of design model could help LoL a lot, but its problems run deeper.
LoL as a game is stuck in a state of transition. On one hand we have the old school content like Urgot, Mordekaiser, Urgot, Ryze, etc. and on the other hand we have all of the game's newer content, like Azir, Yasuo, Jinx, Kalista, etc. These champions really do not fit in the same balance universe because the design standards for everything from mobility to counterplay to number tuning has changed drastically since League's inception. Riot frequently updates their older content, but because there is so much of it and they have decided to stick to LoL instead of doing what DotA did and launching a sequel game that is fresh and new from the start, we are left with a game that is losing some of what gained its initial audience and hasn't yet ironed out what it should ultimately become. This is the Reason League can't have DotA 2 balance. If DotA hadn't launched DotA 2 as a whole new game, they would undoubtedly face similar issues with outdated mechanics and game style, not to mention the fact that it would have a ton of Technical issues much like LoL does because League runs on a comparatively old system.
Things Dota 2 does that League should do better (and can do if Riot puts some effort into it):
- The whole Melee vs Ranged dilemma (you hardly notice when someone is ranged or melee in DotA 2 except in certain lane setups).
- The concept of role (In Dota, roles are much more flexible in general).
- The frequency of patches and balance updates.
- The maleability of the meta (DotA 2 has a lot of different ways to play the map, like Trilanes, Offlanes, Duo lanes, Roaming supports, Designated gankers, etc.).
- All playable characters are unlocked from the get go.