Yes, I do a rinse step, because it gives me another shot at removing contaminants/cleaning fluid residue from the record surface after the first pass of fluid cleaning and vacuum; whatever fluid residue remains after that first pass is itself a contaminant, and ought be removed.
Sometimes, you read of folks who find their records noisier after wet cleaning. Part of this may not be just that the cleaned record reveals more of what is in the grooves, but that a ’bad cleaning’ --leaving fluid residue (which includes the contaminants it is supposed to bond with) on the record--dries on the record and makes things worse.
I buy mainly older records and in strong light, you can see the water spotting left in the deadwax from haphazard wet cleanings where the fluid dried on the record. Since the cleaning fluids contain some sort of surfactant to break surface tension, getting a record dry without removing this fluid will leave some sort of chemical residue even if your cleaning and vacuum step is effective in removing particulates, condensates from fumes (according to those old Percy Wilson papers) and other liquids (beer, old cleaning fluids that weren’t effectively removed, whatever) that are deposited on and dry in the grooves.
In a quick and done wet record cleaning process, the record will get dry but this doesn’t mean that it is clean. Thus, the rinse as follow up step.
I also don’t know what affect leaving some sort of chemical residue on records does, long term. You read of people suffering from bag rash--a chemical interaction between the inner sleeve and the record. There’s various reasons offered for why this occurs- plasticized leaching from the plastic used in the inner sleeve, a combination of heat and pressure of record storage, particular types of plastics used for the inner sleeves, etc. One theory I’ve toyed with--i have no way to prove this-- is that the effects of such haphazard record cleaning and use of after market inner sleeves made of plastics result in some chemical interaction, long term. So, strictly for preservation of the record, long term, I find some comfort in the idea that I’ve done as much as I can to remove that chemical residue.
Truth be told, my cleaning practices weren’t all that sophisticated when wet cleaning became more common by the mid-’80s here in the States with the introduction of the VPI and Nitty Gritty machines. (the Monks was always a rare bird). And sometimes, I’ll pull out and play a record that had been cleaned back then on a VPI RCM, using whatever fluid I was employing at the time, including home brew with a bit of alcohol, and the records play fine and don’t exhibit any bag rash from decades of storage in those old Discwasher VRP sleeves.
For water, I buy Reagent Grade I in bulk, far cheaper than the audiophile branded pure water. But even that may be unnecessary. I interviewed various people at the archival facility of the US Library of Congress several years ago on cleaning and preservation practices. The Library uses D/I water and one preservation specialist there suggested that this was all that was needed.
Keeping brushes or applicators and other materials that come in contact with the record surface clean is also essential in my view. Easy enough to do during and after a cleaning session. I wash the brushes and applicators in a solution of high grade IPA and Reagent I water and also pre-wet and rinse them in advance of cleaning.
Sounds like compulsive behavior but, unless the records have been damaged, they typically play very quietly without clicks, pops or groove noise. (I’ve been successful in getting some records that sounded like they had suffered groove damage to a higher state of play through multiple cleanings, combining conventional wet cleaning and vacuum with ultrasonic cleaning). The combined cleaning methods seem synergistic. Though I’ve varied my practices in small degrees over the last few years, this approach- of multiple cleanings, using different methods, along with a pure water rinse--has improved results for me based on what I hear after this multi-step, multi-process cleaning. Here’s my current set-up, although I was able to get pretty good results using my old VPI and a rinse step.
https://thevinylpress.com/wp-content/uploads/2017/12/DSCF0766.jpg 
