I've read all the points above. Now, I don't have quite as much experience with Fire Emblem as some of you do (played FE7 2 or 3 times, Sacred Stones once through), but I really do love this game so much that it might just be my favorite of the three.
Look, there may be an issue with how intense character customization is. There may also be a problem with having those skirmishes and random encounters. Hell, reclassing is pretty cool, but it might also make characters virtual clones, as you say. There is a grind too, let's not deny it.
Do I think these features are hard to avoid? Yes. Do I think these features in the end had more benefits than drawbacks? Indeed. Do I see why the developers put them in there? Yep. Do I think the game is more accessible to new players? Yes. Does it hurt the gameplay? No--I think they did it in a way so that hardcore fans of the franchise can still enjoy it a hell of a lot.
I actually liked the character customization a lot. Sure, it made commitments get lost a bit, but it made my experience on Hard-classic completely different from my friend's who played on Normal-classic. We saw the same main story, the same characters, but the interactions with each other and how we ended up purposing different characters were completely different. It gave me a sense that I can get a completely different experience on my next playthrough (problem is, I haven't gotten to that second playthrough which shall be on Lunatic because I'm too busy now reaping everything from my Hard-classic playthrough...which is a ton of fun by the way--I currently have 120 hours clocked on it).
Maybe it leads to characters combat-wise being replaceable, but honestly, I think the characters in Awakening were some of the best in the series. I don't recall a single character feeling cliche, and not a single encounter reminded me of a previous one in a previous game (whereas Sacred Stones had several that reminded me of a few characters from FE7, and FE7 had several predictable characters). Take Gaius, for example: a low-life thief with a kind heart? Yeah, we've seen that in several of the FE games before. But then the sweet tooth catches you way off guard, and then what catches you even more off guard is when this sweet tooth isn't just a gimmick--it leads to some really great interactions with other characters! The uniqueness and originality of so many of the characters in Awakening, and all the possible dialogue options (they are all so different too...it's overwhelming so that I can't help but try to unlock as many as I possibly can), it made them feel indispensable to me--I just didn't want to lose any of them, because of the crazy unique experiences they gave me. Also, at least they limit reclassing so that a character that starts out as a certain class can't switch to something that would be so beyond their personality.
Yes, skirmishes and random encounters can unbalance the game. It could make it more forgiving, and can make you get overpowered characters in the end. However, this is just an option available--a hardcore character can choose to ignore them just about as often as he wants. I did a skirmish once in a while, and I did all the children chapters I had available to me (along with the "Gaiden" chapters, which were also a lot of fun), and the main story was STILL really hard for me (partially because I don't like anybody dying--I'll replay the mission if anybody dies). Different players can play in the different styles they want, and that I think led to a better experience overall.
But then let's say it leads to a grind. For me, Fire Emblem Awakening proved two things about games to me recently: (1) DLC is not beyond redemption (FEA, I believe, did DLC very much right, aside from the Golden Pack, which they should've advertised as only for inexperienced characters), and (2) Grind in an RPG is not always bad. I actually found the grind quite fun so as I would do it voluntarily. Random encounters in FE are actually quite fun, and then bonus teams are even more exciting. No battle really ever ends out the same way, after all. Some I choose to do, some I don't. At least they were more fun than in Sacred Stones, when the classes you could fight against were limited. So yeah, there's a grind, but it's optional, and it's not as boring or repetitive as it is in something like Diablo 3 or in several MMOs.
In the end, I think what really keeps FEA being such a loved game to me is that malleability of playstyle, of that near infinite replayability, of all the free DLC and the paid DLC that Nintendo handled so well. The story was actually really strong and memorable to me--it was original, and took on a very different path than the other two FE games I played (which had cool stories but they didn't feel so different from each other). Sure, as YourVeryOwnGeek mentioned, there was a bit of a disconnect in some cutscenes, but I thought the cinematic scenes made up for most of them. Also, the character portraits were still pretty great. The characters were some of the strongest to me, which made up for the fact that combat-wise, many were replaceable. The grind was fun, the skirmishes avoidable, and the difficulty still pretty damn high, especially in Gaiden chapters (I still haven't finished all of them because they're so freakin' hard).
I guess that's the other side of the argument. The game really did strike a really nice chord in my mind. It was VERY different in many ways to other Fire Emblem games, but I was really happy with the change of pace and how it turned this game into something I can go back to over and over again without feeling repetitive.