The tactical philosophy behind the thinly armored M113 APC was that it would be a "battle taxi" which would enable infantry to quickly cross shell/bullet swept ground to close with an objective and to then dismount to secure the objective. It was never intended to be an armored fighting vehicle which would protect the infantry while fighting from it or to offer protection from tank and anti-tank fires. It wasn't designed with a major weapons system and only had a MG to provide some suppressive fire while the infantry was closing with the objective and dismounting.
There was an eternal debate about where the infantry should dismount to fight; in front of, on top of, or beyond the objective. Either way, the infantry would be killed in bunches within the APC, rather than individually on foot while advancing to and assaulting the objective. Fortunately, we never really had to test the operational concept because we never had to fight the Soviets in a major war.
The M113 family certainly did enhance the mobility of the infantry and did offer some degree of protection. It also provided the basis for a wide range of armored utility vehicles, incl TOW tank killers. Our budget driven army is now wedded to the wheeled LAV for better or for worse. The LAV vs M113 is probably a saw-off on automotive reliability, somewhat better on protection, a lot better on its weapon's system, but poorer on cross country mobility.