Mainly because it takes growing energy away from the lime tree above the graft. You want all the energy you can get going to the fruit and tree you are going to be using.

Rootstock is often very vigorous, and if you leave the suckers on they will take over and you will have a rootstock tree (sour orange - probably), not a lime tree.

It is also a different plant than the plant above the graft the reason it being used is the rootstock is immune to a lot of soil deseases. If you let it grow, it is useless for you fruitwise, too seedy, too sour or no fruit at all.

I have a question along the same lines. I bought a key lime tree from someplace like gurneys or something like that and when it came last summer it was tiny with two leaves. Now its grown a lot with branches everywhere. i don't need to prune these branches do i? This is not a grafted tree right? Or is it? I dont guess i really understand what a grafted tree is versus any other kind. Someone please help.

1st determine if the branches are from below the graft union, a swelling at the base of the trunk. If they are below, cut them off, they will take energy away that should be going to the lime. If they are above, it is ok to leave them on unless they are criss-crossing too much; then remove one of the criss-crossers.

Also, begin to think about what you want your tree to look like in several years. [Should be a main trunk with strong side branches at various heights. I assume you want a lime tree not a lime bush.]
To that end, allow at least one branch toward to center of the tree to begin growing straight up, you can get a 10' landscaping pole and loosely tie it to that, with green vinyl stretchy tape. As the tree gets bigger you can begin cutting off the lower branches, say anything lower than 2 feet, unless you have several strong Y-branches low on the trunk. The branches above 2 feet will easily droop to the ground and protect the trunk from sunburn.