Paper doesn't create plumbing problems, though: it adds very little to feces in terms of mass or volume. The trick is in putting the feces (and the paper) somewhere, and unless it can be dissolved on the spot, it has to be transported. Water or some other solvent is needed for moving it in pipes, but it could also be packaged in a container that is then moved along some sort of a tube or set of rails or whatnot, without expending any solvent.
Naturally, transporter tech would take care of either dissolving or relocating or both. Whether it would be too "expensive" or "complex" or not is probably not the question, as water toilets are hellishly expensive today (not the porcelain, but the piping, and never mind the end processes!) and still eagerly purchased - and TNG era people use transporter technology for trivialities such as making coffee or dissolving dishes anyway, so it must be dirt cheap in those futuristic terms.