The biggest issue with getting into Dota 2 right now is that the tutorial is semi-broken and bots aren't in great shape as well. Valve could certainly stand to improve the new player experience some because trying to just jump into online matches immediately is a really poor decision.
I love the game to death (5000+ hours) but totally understand how some people can't get into it. You almost need a friend or someone to show you the ropes.
and it takes like 20 minutes to get to the good stuff.
That's really not right. Dota is an incredibly active game early on with tons of movements happening around the map. Sure, your cores will probably want to minimize moving around early but supports absolutely move around all the time.
I'm not really going to try and compare it to other games just because my experience with them are limited (I've played a little LoL and a little HoTS). I just wanted to dismiss this idea that Dota is somehow nothing but 20 minutes of AFK farming and then fighting. It's more complex and active then that.
(Also I found HoTS incredibly dull. but w/e)