When I 4L80E swapped my red truck I kept the radiator's internal transmission cooler functional and installed a Tru-Cool M7B AUX cooler in addition. My line of thinking was that if the transmission fluid temperature ever spiked rapidly for some reason then having the radiator cooler would probably help bring it down faster than just the AUX cooler. I understand why some people bypass the radiator cooler and if I ever have issues with one I may consider doing the same, but I haven't so I didn't. (Knock on wood)
I would consider installing a different AUX cooler with a fluid thermostat if you want to continue to bypass the radiator cooler. The Tru-Cool M7B I mentioned can be fitted using the factory AUX cooler brackets if you trim them a little. Instructions to do so can be found here:
https://www.gmt400.com/threads/how-to-factory-auxiliary-trans-cooler-upgrade.18104/
A few other members here have installed much larger coolers as well.
@Curt is in the process of installing a Tru-Cool 40K which is massive.
https://www.gmt400.com/threads/time-to-get-serious-with-4l60e-4l65e-cooling.50138/