My solution is that there should be a bidet in every bathroom. If you're unsure what a bidet is, quite plainly it is a low mounted sink that sprays your butt off after you go to the bathroom, thereby skipping the step of wiping. Not everyone can afford a bidet, but people who can afford one should go out of their way to get one. We are in America, and we are above the inferior hygiene caused by the usage of toilet paper.
Like I said earlier, maybe toilet paper isn't totally obsolete, but it should be obsolete as our main source of anal hygiene. Rather, it should be an auxiliary for after the bidet has been used.