I have read that the reason they use the rad is that the coolant temp will bring the transmiison fluid up to operating temperatures quicker at start up.
What type of radiator fan are you using? Does the 2004R have a stock size or deep pan? Does the pan have cooling fins or tubes? Has the trans been rollerized as part of its build up?
AllStar performance triple pass aluminum without a transmission cooler. It has a stock pan without fins or tubes. I'm not sure what you mean by rollerized, but the phrase my transmission guy uses is it has more billet parts than non-billet parts lol.
That is one major factor, most wear occurs at cold start up. The other is that heat conduction from liquid to liquid is about 32 times faster than liquid to air heat radiation, a higher delta P. Most aftermarket external trans coolers are designed and intended to be auxiliary coolers and are marketed as such. They are not designed to be the primary and sole cooler for a trans. One can get away with bypassing the rad cooler at the expense of running a much larger external cooler. Many transmission specialists like PATC recommend keeping the rad cooler plumbed in for this reason.
I've never heard either of these statements, but it seems logical. My trans guy has no concern about an external cooler only. And FWIW, we have had to replace the 3rd/4th clutches a couple of times. Mostly due to it will make a ton of go without being near WOT, which it needs to be over 70% throttle to develop max line pressure. But the turbo doesn't care where the throttle is once the motor starts making heat and rpm (air flow). It can open the gates at 50% throttle. My son drives it 95% of the time and it takes some discipline to keep the boost down with low throttle position. Hence, smoked/burned clutch packs.