if I had all the answers...
adrian
i like your persevering attitude.
If I knew all the reasons why a multipart multimaterial hose were deemed bad, I might be already making a living as an exam-question writer for Master Plumber certification exams. Example: "List all seven reasons why ... is dangerous."
You asked "Are you saying that the answer is that it might leak due to all those extra splices? "
Can we agree that we both don't know for sure but that we both think that that is a sufficient reason -- all by itself -- to agree that the pipe could be deemed not up to snuff if it were for a new installation being prepared for a new buyer who would be expecting a clean and professional installation? I think so. Can we agree that "Code" is designed to produce that level of cleanliness and professionalism? I think so. Is there more? I don't know for sure, but I think we have studied this enough to wear out just about 99% of the population, if anyone is following this thread. Even the most dogged scientific researchers could ask why we want to know more.
If there were any other reason More serious, you would have heard it by now, I believe. Anyone can correct me if I have missed something important. I know for sure two things: 1.) it works for now, and 2.) you asked if consensus would be in favor of your changing it, and why.
Next subject. "Why is passage through the disposer bad? (Because the disposer might be full of crud?) So the idea is to tee into the other drain that doesn't have a disposer on it? Without a conventional air gap of some kind couldn't such an installation siphon water out of the sink back into the dishwasher?" -- Yes. Almost. Not quite. Close. The disposer may be full, and or it may do other bad things, and or the sink and or the dishwasher may also do bad things. Cross-connections and backflows possible everywhere. Rarely happens but can be fatal, lethal, deadly. It can be a matter of life or death. That is what plumbing is about. In my view, it is more complex than electricity which is also extremely dangerous.
Look at any installation with NO disposer, and then look at my remarks as saying "can we do the same thing WITH a disposer present, by just not going through the disposer?" I am not a plumber so I ask without knowing the answer.
Drinking water never kills anyone, until suddenly one day it kills people. Contamination. Sewer gases never kill anyone until suddenly they do. That's plumbing! (Sewer gases are sometimes odorless and lethal). A cross connection is never going to cause a problem until one day it just does. Suddenly one day it can really, practically, seriously and lethally cause a "public health problem". Although the probability is low, who will guarantee you that No one will ever sue you and that you will never feel guilty about your plumbing? As you are persistent, perfectionist and persevering, you may appreciate my telling you what I think may help.
Conclusion: air gap is a good thing. With no garbage disposer, it is easy to hide, in the drain.
David