Jeff,
I agree that we need to keep things in perspective, and this is my perspective. The average human probably weights about 150 pounds, while the average cat probably weighs about 10 pounds. Thus, there is a significant difference in the amount of a substance needed to produce deleterious systemic effects. Thus, what you refer to as a "trace amount" may indeed not be harmful to humans, but may very well be harmful to cats. Also - I wash my counters with plain water after cleaning, so I don't get any amount of cleanser in my mouth. I suspect others do the same.
You have also not addressed the issue of localized (as opposed to systemic) effects at all. The mouths of both cats and humans are lined with mucous membranes, which are particularly susceptible to damage by caustic and acidic chemicals. The solution contained in the factory Litterfree cartridges (and virtually all other cleaning solutions) does not have a neutral Ph (the Ph of Roccal-D, which is widely believed to be the active ingredient in the Litterfree cartridges, has a Ph ranging from 6.5 [slightly acidic] to 9 [highly alkaline]; a Ph of 7 is neutral), and thus has the potential to create localized damage to the mucosa in the mouth even in the absence of systemic damage. This is not good for the cat.
The MSDS for Roccal-D can be viewed here:
http://www.sefsc.noaa.gov/HTMLdocs/Roccal.htm
The advantage of using dishwashing detergent is twofold. First, the manufacturer has clearly contemplated that at least SOME people will ingest small quantities of it (since not everyone washes their dishes thoroughly), and the Ph of such substances is neutral or very close to it as a result - the manufacturer has an interest in avoiding legal liability. Second, by not placing it in the cartridge and instead adding it at the beginning of a cycle, one can be reasonably assured that that the vast majority if not all of it will be rinsed out by subsequent cycles.
I prefer to err on the side of caution.