The Spencer wasn't really that limited, compared to others.

Anyways, the biggest reason they were not used on a large scale was mostly cost. The guns were expensive. Some were not robust enough for military use and they were more complex to maintain for the everyday soldier. So if it gets broken, you have to pay to have it repaired or replaced. The ammo was also fairly expensive and a developing technology still. Also, some generals, but mostly politicians, didn't want to spend the extra money for the increased ammo expenditures in combat. They felt that soldiers would just blow through their ammunition.