Overall play is kind of a nebulous thing, isn't it? Seems like it's just an easy to way to justify the performances the players you like, and to slam the players you don't. It's almost entirely subjective, and just about anyone's stats can be used to demonstrate that they are either good or bad, depending on your argument.
For a long time, Walcott justified his inclusion by scoring and setting up goals. That proved his "overall play" was good enough. He absolutely could've been a starter for us in a title winning side. Injuries lessened his abilities and that chance was gone. The game has changed and his skill set is even less sought after, now.
I think the idea of player intelligence, especially on this forum, is vastly overrated, and maybe not even real. I mean, I think they're all idiots, on the pitch and off it, so being the smartest of a bunch of dolts isn't exactly something to crow about. It's kind of like how English pundits are so obsessed with "hard work". At the speed that the game is played it's all about talent, instinct and learned behaviors. One is the product of coaching, and the others can be honed by good coaching. Not to mention the collective aspect, which really waters down individual players abilities to influence games as much as we like to believe they can.
The smartest, most technically adept player is less likely to influence a game's outcome than one that just scores and assists. Then again, those could be the same player. So much of it depends, in the end, on the whole team and how it's set up to play, that singling out individual traits of this or that player's game becomes pointless without the overall context.