While the idea of character-independent abilities in Final Fantasy have been around for a while now, dating back to Final Fantasy II, but its execution has usually been, for better or worse, flawed, and its implementation in Final Fantasy VII is no different.
Following the introduction of Espers in Final Fantasy VI, many of which would go on to become the ever-popular summons (although a number of them had been previously seen in Final Fantasy IV), the decision to make all abilities similar to Espers in Final Fantasy VII was not exactly a good way to go about it. Unlike Final Fantasy VI, where Espers could only be summoned once but the spells they granted were limited by only the user's MP, the usage of Materia in Final Fantasy VII as limited by the player's level of mastery over the given Materia as well as their MP pool, often to a single use on a freshly procured Materia, which fundamentally limited what a player could do with the Materia at hand; while this encouraged pre-planning, it also restricted the flexibility available to players greatly, forcing them to investing large amounts of time in-game to grinding and mastering their Materia, rather than forwarding the story and such.
While the idea of linking Materia together was and is innovative, its implementation was a bit short of perfect; by implementing a linear system of linkage, SQUARE severely limited what players could do with creative Materia linking, and while links are possible in Final Fantasy VII, a grid format, or even a three-dimensional method, would have added much depth to an otherwise flat system, where almost every high-end character is linked in nearly the same fashion.
Ultimately, Final Fantasy VII was a victim to SQUARE's success with the franchise as a whole; following the success of Final Fantasy VI, which garnered much critical acclaim for its Esper system, SQUARE's attempt to duplicate the system by modifying its fundamental flaws without keeping many of its strengths proved to be a difficult pill for some gamers, such as myself, to swallow. While the gameplay is by no means broken, it still sadly falls short of what came before it; by completely eliminating character-unique abilities aside from Limit Breaks, which were no more than differently animated attacks of superior power with the exception of Cait Sith, Aerith Gainsborough, Tifa Lockheart and Vincent Valentine, characters lacked the uniqueness of those in Final Fantasy VI, where characters such as Locke could steal while Leo could use gadgetry to do a number of things to enemies. Even though a similar critique can be leveled towards Final Fantasy VIII, which I prefer over Final Fantasy VII, the Limit Breaks for characters in Final Fantasy VIII were more innovative in their execution and variety than those in Final Fantasy VII; in the case of the latter, the general execution of the Limit Breaks in Final Fantasy VII were generally limited to selecting the desired attack and watching it go, Limit Breaks in Final Fantasy VIII showcased a number that required additional input to properly execute, while others gave players options otherwise unavailable outside of the Limit Break. However, that's mostly off-topic, so it should be addressed in another thread entirely.