Windows and applications may expect a paging file too, so there can be problems with eliminating a paging file completely. I've done it before and things seemed to more or less work, but I never saw a noticeable improvement.
If you have enough memory to do what needs to be done, then the paging file shouldn't get used anyway. If you don't have enough memory or you have an application that requires a swap file, you're going to want to have it be available.
Having a decent amount of memory will help reduce hard drive usage, but its going to be hard to eliminate it. Many/most apps don't preload everything they need to run when they start, they just go get it when/if they need it off the hard drive.