3e’s introduction of Prestige Classes was a kind of neat idea, full of promise, that never really paid off. Most of them were bad, and a few of them were truly broken, and in large part they ended up existing solely to see what kind of abusive combinations people could come up with.
At first glance, Paragon Paths and Epic Destinies were supposed to fix that, and they kind of do. Since they can’t be combined the way Prestige Classes were, there’s less room for abuse, and since everyone gets them (and they’re layered on top of your normal class) it seems more equitable. And mechanically, it mostly works out. There are a few exceptions – every “broken” character I’ve seen for 4e depends on one or more of the three unique sources of powers (Race, Paragon path and Epic Destiny) combined in weird ways, but even those have usually depended on a creative misreading of the rules. By and large, they’re a mechanical improvement.
But they still fall flat for me. This is another case of the color going one way and the system going another, and someday I’ll make peace with that, but probably not today. The thing is this: some paragon paths are transparently just wrappers around a mechanic but most of them have some element of story to them. Yes, sometimes that story is a bit of a headscratcher, but mostly they’re interesting elements that might add something fun to the world. But that’s where the break down. First, if the powers for the PP are a bad match for your character, it doesn’t matter HOW good the color is, it’s not worth picking up. The powers are just too important to play to pick something blatantly ineffective. Other games can support non-optimal choices to varying degrees, but not 4E.
Second, since this choice is not made until 11th level, any plot elements that the Paragon path introduce end up coming out of left field. If I knew from the outset that a player was going to pick a particular Paragon Path, then it would be possible to introduce those elements into play over the course of the game. If you’re going to become a pit fighter, maybe I’ll have you fight in a pit. If you’re going to join the Cerulean Order, maybe I’ll actually take steps to actually introduce the Cerulean Order into the game.
As with many things in 4E, the first problem is easily enough solved with reskinning. Just say to the GM “I want the background from this Paragon path, but the powers from this Paragon Path” and bam, you’re good. It might take a little tweaking, so a Dwarven Kensai might actually be a an axe-master, but that’s pretty trivial.
Solving the second problem’s a little more involved. You could just have players tell you what Paragon path they’re going for, but in many cases they may not know yet. Back when I was actually writing 4e Products I had an idea I rather liked which I know throw out into the wild. I always thought that Paragon Paths could come with feats, or more specifically, one feat per Paragon Path, offering something useful that synced with the powers and abilities of the Paragon Path. They’d be on the same level as racial feats, that is to say, intentionally a little bit better than regular feats because they reinforce a theme. They’d be handy for characters and, more importantly, they would flag to the DM that the player was going in that direction, so he could start introducing those elements earlier on in the game.
All of these concerns apply to epic destinies as well, and there’s a case t be made that the same solutions could apply. I could see it. But I admit I’m tempted to do something weirder and just let players pick up Epic Destinies at level 1 (as if level 1 were level 21).
Sounds dangerous, I know. Players will get some kind of death resistance and may pick up a big whammy of a power, but to be frank, it’s only one whammy (and in many cases, it’s not much of a whammy, since it tends to rely on other powers – though it may then be many whammies). It’s a power bump, no question, but it also lets you START stories about the children of gods and chosen saints rather than discover those stories 20 levels in. 
Honestly, I like the direction that Paragon Paths and Epic Destinies seem to indicate. And if you actually just want to start a game at level 11 or 21, they work fantastically, at least in part because they suggest that the history of the character has lead to this starting point. It's my hope that, with a little tweaking, that that can also be accomplished through play.
1- And I’m ok with this. Honest crunch is not a bad thing.
2- If the mechanical element worries you, spread out the rewards so they’re over 30 levels not 10, and that should mitigate things enough.