This is a great (and I mean really great) question, because it has been debated by historians themselves for years. It really does seem at first glance that the Roman legions of the early Empire would have benefitted from having their infantry make use of longer swords to combat their enemies. A longer reach would have allowed them to strike at their foes from a greater distance, and perhaps allow for stronger and more deadly strikes that might have killed the opponent right off the bat.

That is, until you consider the one thing that almost every Roman historian praises when they brag about their Empire's legions: discipline. To quote our good friend Vegetius:

Victory in war does not depend entirely upon numbers or mere courage; only skill and discipline will insure it. We find that the Romans owed the conquest of the world to no other cause than continual military training, exact observance of discipline in their camps and unwearied cultivation of the other arts of war. Without these, what chance would the inconsiderable numbers of the Roman armies have had against the multitudes of the Gauls? Or with what success would their small size have been opposed to the prodigious stature of the Germans? The Spaniards surpassed us not only in numbers, but in physical strength. We were always inferior to the Africans in wealth and unequal to them in deception and stratagem. And the Greeks, indisputably, were far superior to us in skill in arts and all kinds of knowledge.

The gladius was a weapon that was designed for precision and control, to be used by disciplined soldiers defended by a powerful, coherent, tight-knit shield wall that advanced across the battlefield like a proverbial juggernaut. The exacting nature of Imperial discipline provided that the attacks of their soldiers were to be clean, precise, and deadly. A Roman legionnaire bore the brunt of an enemy's attack with his shield and his heavy armor, and then, when he saw an opening, ended his foe's life with a quick, precision stab with his gladius to the center of the neck or upwards under the ribcage to the heart and lungs. The great thing about attacking with a gladius being that the thrusting attacks did not interfere with the Roman battle line, and allowed the legionaries to keep tight cohesion in battle. This is the primary advantage that the gladius had over the spatha. One also might also argue that the other advantage to the gladius was that it was cheap to manufacture, and was light in the hand (which was to make up for the fact that the semi-cylindrical scuta were quite heavy as far as shields go.)

In contrast, the spatha was a weapon that was adopted/designed to increase the striking reach of the Roman cavalry, where a gladius would have been impractical, since it is almost useless for a cavalryman to strike an enemy with a thrusting attack using anything else but a spear or lance. By the time the spatha became popular amongst the infantry in the late 3rd Century, there had been significant changes to the legions, one of the most notable being that the legions became smaller and more mobile. This trend continued throughout the 4th and 5th Centuries, as the legions (then split into various groups of limitanei, comitatenses, foederati, mercenaries, retinues, etc.) became generally more reactionary, than proactive. The breakdown of discipline in the legions decreased the reliability and coherency of the Roman battle line, making the spatha a better choice for the individual fighter, as opposed to the gladius, which really only worked well when used in tight coherency.

However, the most significant reason why the spatha was adopted was because the significant infiltration of the military by the Germanic peoples starting in the 3rd Century AD. On the average, these peoples were taller and perhaps stronger than the average Mediterranean person, meaning that their primary advantage was in their reach and the strength of their swing. It is said that the Germans fought as individuals, in loose formation, to allow for greater maneuverability in battle and this style of fighting favored longer swords. So, when the Germans became the majority within the Roman legions, these fighting styles were adopted and eventually superseded the traditional fighting tactics of the Romans. The spatha, which was similar to the traditional fighting weapons of the Germanic peoples, naturally was preferred by them. The ubiquity of these weapons throughout the Late, Christianized Empire was what ultimately allowed them to supersede the gladius to become the standard military armament of both Roman and Byzantine infantry for over a millennium.