the slight performance benefit of having the rad outside in no way makes up for the inconvenience.
I was thinking more along the lines of having a big radiator in cooler air would remove the need for cooling fans.
I have done both over the years and generally found that the slight performance benefit of having the rad outside in no way makes up for the inconvenience.

External watercooling gives you more options than internal. If the radiator is outside the house, it's all kinds of win in winter. If you can put the radiator(s), pump, fans in another room - you've moved most of the noise to somewhere far away from your desk.
I agree with rjk, radiators should be hidden. They just don't have to be hidden in the same box as the rest of the hardware.
Outside the house? That is a bit extreme lol.
