DOTA2's problem is it tries to do everything DOTA1 did, even when DOTA1 did something terrible. A simple example is Player colors. Why? No one cares. Don't believe me? Play LoL for 30 minutes and you'll realize player colors add nothing to the game but make it HARDER to quickly tell allies and enemies apart. Color-coding stuff only works well when there aren't 10+ different color-codes. Just make friendly green, enemy red, like any sane game. Throw in color-blind colors and you'll improve the play-ability of that game greater for new player, and have zero impact on existing players.
Player Colors are not that big of a deal honestly. It's the same 5 colors for each team forever, and gives you an easy way to remember who your allies are by color-coding them in your mind. A quick glance at the map and you can instantly see where everybody is. This is especially useful in high-tier competitive games if you've assigned your whole team to a specific color. LoL gets around this problem by putting a little picture of the hero instead, but honestly it's often difficulty to tell who is who at a glance, especially if they're overlapping each other. Basically, DotA's way is much more elegant and streamlined, it just takes more skill and time on behalf of the player to use it correctly.
That's basically DotA vs. LoL in a nutshell. DotA will always take the path of skill and complexity, LoL will always take the path of convenience and simplification, it's just the difference in the two design philosophies.
DotA 2 can't use LoL's item shop because DotA's items are so much more complex and varied. It might be great in LoL for each item to be characterized under "health", "damage", "mana", etc., but DotA's items don't fall into those neat little categories. For example, the cheapest item in the game, a +1 stat branch, gives you a bit of health, health regeneration, damage, attack speed, armor, mana, and mana regeneration. Are you really going to put such a simple item under all those categories? If you were to put every item in every category it corresponded to, it would be even messier than it is now.
Where LoL's items scale up, DotA's items scale down. In LoL, the more expensive an item is, the more cost efficient it is, where in DotA, the more expensive an item is, the less cost efficient it is. This means that in DotA you're almost always using all your inventory slots, and that the low-tier items are just as, or more important than the lategame items. There are much less "cookie cutter" builds, or just rushing for a specific powerful item every time. On the other hand, it means you need to have a better knowledge of what all the items do since you can't just rush for the same thing every time. DotA also has many more activateable items as well, so there's a lot more complexity in terms of actually using them instead of them all just having passive effects.
I've played over a thousand hours of LoL, HoN, and DotA, and when I think about LoL and DotA 2, it's like comparing Homeworld 2 to AI War. You're going to pick up Homeworld 2 much faster; it's the much simpler, more streamlined, and easier to understand experience. Within 10 minutes you can have the hang of it and while you can get significantly better, the lack of complexity in the game means eventually you'll hit a peak and not grow much above that. DotA is like AI War - to new players it's probably going to be incredibly frustrating to start out with. You're going to get your ass handed to you...a lot. It's going to take weeks or even months to learn all of the ships, strategies, minor factions, AI Types, etc. - but if you stick with it long enough, the experience will be so much more rewarding and gratifying than if you had just said "Awww this is too hard, I think I'll stick with Homeworld 2." In addition, the level at which you can personally grow (skill cap) is much higher. I've been playing DotA for 9 years (since I was 16) and I still feel like I have so much room to improve. I played LoL for less than 2 years, and most the time if I lost it's because my team wasn't doing their job. That doesn't mean I never made mistakes or couldn't have gotten better, it's just that I had hit a wall. The miniscule amount I may improve for every hour of LoL is nothing compared to the amount I improve for every hour of DotA.
The game pacing of DotA 2 is much faster as well. While I realize this may be something some of you dislike, it keeps the game much more hardcore and action packed than LoL. There's no Flashing out of ganks or hiding behind your tower and expecting to be completely safe. If you're on the map, you're vulnerable, but the enemies are too. There's items like Smoke which render an entire team invisible to make ganking and initiating team fights easier. There's mechanics like reliable gold which means you get to keep your gold when you kill an enemy while he loses his.
Like I said, they're different games, but if you really invest the time into DotA 2, I think you'll find it was completely worth it. I've literally never heard a story of somebody who spent 100 hours of playing DotA 2 then went back to LoL. I hear countless stories of people playing 1 or 2 games of DotA 2 then quitting forever. It's just like anything in life, nothing good comes without hard work and dedication ;p