My guess is that Roddenberry had plans for the character, but as his health declined and his involvement in the show was reduced, the remaining producers did not have the heart to get rid of Wesley. It seemed like Wesley was mostly written out and sent off to Starfleet Academy almost immediately after Roddenberry died.
IIRC (from somewhere/when I don't recall) Wesley was Gene's ideal of what the perfect Federation citizen would be - the template for how humanity had evolved beyond basically everything that made for good drama. The end result came off as an insufferable know-it-all.
It's unfortunate that so much of the hatred for Wesley transferred to Wil Wheaton for so long. He's come out from under it since, but a lot of trekkies hated Wil just because of the role he played.
