Lets try and be absolutely clear; You need to take distance into account if you are planning a descent. You seem to have a problem with that.
I might be wrong but where in the sentences like "Losing 5000 feet takes 15 nm according to the 3X rule." did I leave out the distance?
Although I'm beginning to get a feel for our mutual misunderstanding. My assumption in my posts (and A&Cs posts) is that you are cruising along with the DME or the GPS telling you the distance to your target. At some point in time you need to start your descent, and you want that descent to be a comfortable one at a three degree slope. So you calculate the distance from TOD to the target using the 3X rule and at that point in time you either start your descent (using the numbers appropriate for a three degree slope in your aircraft type) or you gently remind ATC that you would like to start your descent right now.
Your assumption might be different. What I feel is that you are not calculating a TOD point in advance, but are suddenly confronted with a wish or ATC instruction to be x foot lower in y nm. In that case, indeed, the 3X rule does not work at all and you need a different calculation (either based on distance or time to the target, it doesn't matter) to calculate the actual ROD needed to be level at the desired altitude, at the desired distance. Nothing to do with the aircraft type or speed, but simply by the fact that losing x foot in y nm might need something other than a three degree glideslope.
So here's my opinion: The 3X rule can be used (and is being used) to calculate your TOD point in advance and it works for virtually all aircraft, because it leads to a three (point thirteen) degree glidepath. However, because of external circumstances you might not be able to start your descent at the optimum point. In that case you need a different calculation to calculate your actual needed ROD, based on the actual distance to cover and your actual groundspeed.
Now what I don't get in your posts is why you tie any of the calculations (both the 3X rule and yours) to specific aircraft types. You say "For cessna's and the like i used to taech groundspeed/distance = minutes and divide by altitude to lose." Absolutely correct, but the exact same method can be used for A380s as well.
Likewise, about the 3X rule you say "All I am trying to get across is that it clearly is a good rule of thumb for faster aircraft but is mathematically incorrect for smaller one. The figures prove that without question." Now I did run the numbers for you, got descent rates between 333 and 527 fpm for small aircraft, when using the 3X rule, which you find entirely acceptable. Yet you maintain that they are mathematically incorrect?
So, please, for my sake and the rest of this community, could you come up with a scenario where the 3X rule is NOT appropriate for a small aircraft, but is appropriate for a fast aircraft, all circumstances being equal? And keep in mind of course the reason for using the 3X rule: to calculate the TOD point in advance.