> To come back to my question, since they have no gravitational pull
This is not true. The curvature of spacetime is still non-trivial near a naked singularity, and so there is certainly gravity. A superextremal Kerr black hole, for instance, functions just like any other mass from a sufficient distance. Objects can orbit the singularity just fine.
> For those of you who don't know, naked singularities are basically theoretical black holes without an event horizon, so you would be able to see the singularity inside directly.
A naked singularity is simply a gravitational singularity not enclosed within an event horizon. So the big bang singularity is, in fact, a naked singularity. The singularity of a super-extremal Kerr black hole is also a naked singularity. In principle, you could travel arbitrarily close to the singularity and then come back. (For a super-extremal charged black hole, the singularity is actually repulsive at sufficiently small distances, independent of the sign of the electric charge. No free-falling particle can actually ever reach the naked singularity in such a black hole. To get arbitrarily close, you would have to have a rocket and actually apply some non-zero thrust.)
The singularity is still, well, a singularity. So paths that lead into the singularity cannot necessarily be extended beyond the singularity. This presents some problems regarding whether these singularities can exist in nature. For one, this means that it would be possible to observe a star or other massive object collapse into an object of infinite density (and this can actually be witnessed since the singularity is not beyond an event horizon). Of course, all current theories of gravitational collapse would leave the singularity hidden behind an event horizon. So it's not clear how a naked singularity, other than the big bang, could ever occur naturally.
A naked singularity should probably be completely black as well. Just as null geodesics leading into the singularity cannot be extended, there's no meaningful notion of null geodesics leading out of the singularity. So the singularity should not emit any light of any kind.
Currently we don't know whether naked singularities could even exist. Right now we don't know of any mechanism that could lead to their existence, and other than the big bang, we don't know of any that actually do exist. (This is captured in the *cosmic censorship hypothesis*, which proposes that all singularities, other than the big bang, must be enclosed by an event horizon.) The cosmic censorship hypothesis is not a proven fact though, it is just a hypothesis. It may well be the case that quantum gravity shows naked singularities to be a real thing.