I think it ultimately depends on what AJ Styles himself wants.
Before getting into that, I think I need to address a few reasons as wo why some hasve said he shouldn't come to WWE or why he automatically just wouldn't make it. The arguments of a wrestler not having "the size" or "the look" is really becoming an outdated and obsolete one when you look at much of the WWE roster. If Styles doesn't have the look or the size, then how is it that wrestlers like Bret Hart, Shawn Michaels, Ric Flair, Chris Jericho, Rey Mysterio, Christian, CM Punk, Daniel Bryan & a whole host of other wrestlers 230 pounds or less have gone onto become World Champions? Some of those guys listed are legit legends, some have the potential to be and some are among the most popular wrestlers on the WWE roster. None of them are especially big guys by traditional pro wrestling standards. Of all those listed, with the exception of Rey Mysterio, they tend to fall in the 5'10-6'0" and 200-220 pound range on average. AJ Styles fits right into that rage. If Styles doesn't have "the look" or "the size", then I fail to see how these guys have made it. Styles is a young, nice looking guy in great physical shape. Again, fits right in with those others.
I will agree, however, that Styles' shortcomings have always lied within his mic skills. He's better than he used to be. He used to be John Morrison bad on the mic. He was flat out awful. However, he has improved on the mic but he's not on the level of most of those guys I listed. If he put in some more work on the mic, I think Styles could continue to improve. He's capable of delivering intense, passionate promos under the right circumstances because he's done it before. His mic skills aren't great, I grant that, but they're certainly not at the horrible level they once were.
Also, I don't know why some want to automatically assume that he won't "be used right". Honestly, it's another old IWC chesnut that gets tossed around so casually, like the size arguments, that it almost has no meaning. It seems that whenever someone is announced as coming to WWE or the topic is brought up of someone coming to WWE, some people always go this route and all but come flat out in saying that WWE doesn't use anyone "right". That's not to say that it wouldn't happen, however, because it can happen to anyone. WWE has used some guys improperly in my opinion. However, so does every other company for that matter. In every wrestling company, there are always wrestlers that have fans who view the wrestling company as not using said wrestlers properly. Every so often, it's true. Most of the time, in my view, it's generally the opinion of fans who are mostly pissed that a wrestler they like isn't being used the way they think he should be. A lot of former WWE guys went to TNA, for instance, and they didn't get "used right" either. Matt Hardy's run in TNA was nothing short of mediocre and became such an embarassment to them that they let him go. Tommy Dreamer and many of the better known former ECW guys came to TNA with Dreamer giving the same promo about how much he's sacrificed for wrestling while bawling his eyes out. They stayed around long enough for TNA to put on an ECW tribute ppv basically and most of them were out on their ass. Dreamer didn't stick around long after that.
As to whether or not he should come to WWE or express interest in coming to WWE, it all depends upon what Styles himself is after. If Styles is happy with the money he's making and his overall place in wrestling history, then he should stay with TNA. He's said time and time again that he's loyal to TNA and that he's a TNA guy. Unless something truly horrendous happens to cause a MASSIVE fallout, Styles will one day be in the TNA Hall of Fame. He's generally thought of as the heart of TNA anyhow and if he did leave TNA, it'd be a massive blow on a personal & emotional level for a lot of long time TNA fans.
If Styles is someone, however, that wants to have an opportunity to really take his place among the "all time greats" someday, he should at least try to head to WWE. I'm not saying that it's not a guarantee that Styles will be "used right" or that he'll rise to the level of a huge star, but he'd at least have the chance. The fact that Styles has been such a key player in TNA for so long is a good indicator that WWE would want to make the most of signing him, if they could sign him that is. If Styles stays in TNA, he's never going to be looked at with the same level of star power guys like Jericho, Orton, Cena, Sheamus or Punk. I'm not saying this to slam TNA but the simple truth is that TNA doesn't have the audience or the name brand of WWE. If you ask an average American about pro wrestling, WWE is what the VAST VAST majority will think. Even people that don't know jack about wrestling here in the states have at least heard of WWE and basically know what it is. TNA doesn't have any of that right now. It might be on that same level as WWE someday, but that's going to be many years in the future. By that time, it won't do AJ Styles any good because he'll be too old to benefit from it. If TNA is still around at that time, they'll have newer & younger faces on the scene. He'll be thought of as a TNA legend but someone that's a huge star in WWE is often thought of as a wrestling legend altogether. WWE has the history, the audience size, the brand recognition and the capability to potentially catapult Styles to another star level in wrestling. As of right now, TNA doesn't. That's just how it is.