Rinse agents do alot for aiding not only rinsing of the detergents but leaving the fiber softer, with more loft and setting the fiber up for bettery drying. Saying that water will remove all is kind of mis-leading. I have cleaned professionally nearly every kind fo carpet fiber. For 3 years with just water. I then pushed the company to test rinsing agents the difference is significant and cam out to somthing like .004 cents a square foot. I finished out the last 6 years using either or rinse agent or rinse detergent.
Generally rinse agents are a 6-6.5 on the acidic side of the scale, they do an excelent job of removing surfactants (the wetting agents preconditioners leave in carpets, the very things that lead to longer dry times) Left over detergents (detergents left in the carpet will as they dry attract dirt and make a sticky residue.) Many also contain a light softening agent that gives fiber a new look and feel. They also help remove left over emulsified solvents that are common in good preconditioners.
Generally detergents range around 10-13 ph. depending on what kind of detergent or fiber you use. They will leave surfactants, detergents, and solvents. These three things will leave the carpet wetter and more capable of resoiling.
Extraction detergents are generaly a step down from teh above. They most often are granular, and will mix at extremely high ratios. They usually are a 8.5-9 on the ph scale but contain no solvents or surfactants. They generally will remove the two former and set the carpet up for drying.
Water setting a stain is also somewhat misleading. Heat can set a dye stain, Generally wet heat will aid in their removal of most soil stains. Wet heat can set dye stains, but it is not the primary way one should remove dye stains anyway. Dye stains can not in most cases be removed with detergents. They must be removed with process that changes their makeup or oxidizes them. IE red, coffee, natural dyes, urine for oxidizers, Rust, for changing the chemical make up.
As for suds in an extractor. Ith recovery hose goes to a waste tank nothing more. As for a rinse agent going through the solution tank, well why do you think they call it a solution tank. The only issue that might arise is iff you tried to put any kind of solvent, Delimonine is a common cause of this. Solvents will ruin the diaphrams on pumps. Solvents are not rinse agents. Putting an extraction detergent or rinse agent into a solution tank is not going to harm it. Hell my previous boss is still using his original HWE that are 21 years old. Yes they have had new vacuums but the pumps are fine.