At the risk of starting a major argument, I think there's a lot more to why they need to make a remake of FFVII than just a graphical overhaul. Even the creators of the game and Kitase specifically have stated the game was rushed and the story incomplete. Hence why so many sequels were made to try to complete the story. More than any other Final Fantasy game, FFVII needs a remake just to fix the games story, along with the graphics.
But more than that, I personally feel the game has problems in other areas. They need to improve the flow of the game as well as the gameplay engine. The flow of the game needs improving simply because about half the game feels like a lot of pointless side quests or forced extra junk not tied to the story (Yuffie stealing your materia, cloud and tifa go 'missing', searching for Big Materia, constant Jenova attacks....). And the gameplay engine could use some real improvement. Even FFVI felt more insppired and for much of the game, FFVII boiled down to the classic spaming attack and heal until you ran into a boss who could only be defeated with a certain Materia.
In all ways, FFVII has definitely shown its age. Unlike the other two PSX Final Fantasy games or even FFVI on the SNES, which are still quite playable.