Topic: Would it improve my airflow to add a rear exhaust fan?

Just to put my situation in context, however boring this first part might be to read, cough, so feel free to skip to my question in the end.

I'm truth be told not a fan of the increasing power demands of modern gaming systems, even though i used to build my gaming pc's around the cutting edge of available technology. Though admittedly only spending up to a certain amount of money before the benefit of the extra performance was outweighed by a too huge increase in cost or power draw. My last flagship GPU was the 2080ti and i would have continued to buy flagship models if it wasnt for the huge increase in power draw the 3090 and later the 4090 and 5090 would require, even though they typically didnt draw power all the way up to the 600W limit. Maybe also a bit paranoid about the lifespan of those huge GPU's since my Asus 2080TI Strix died on me, being only the second graphics card i've ever owned to give up its life. Cant actually recall which other card i've lost during the last many years, but i've been building pc's ever since the mid 90'ies.

My current setup
Fractal Design Torrent cabinet
Intel 12700K + Arctic Cooling Liquid Freezer II CPU Water Cooler (360mm radiator) with the radiator/fans placed as front intake.
Asus TUF 4080 OC, which is placed near the bottom of the cabinet due to the motherboard.
3 Bottom fans set to pull air into the cabinet.
There's no fan in the rear, but there's free passage for air to flow out that way, due to the design of the cabinet.

So my questions: I'm unsure about if it might be a bad idea to let the radiator with the fans pull the air in from the front, since i'm worried it will heat up the air, which passes through the radiator and further into the cabinet. Maybe its better to place it at the rear and have it push the air out instead and have normal fans placed to pull air in from the front?

Or could i just add a top rear fan, to increase the cooling of the cabinet?

I'm also concerned about that the fresh and cool airflow from the bottom is escaping out the rear before it really hits the GPU, since most of the rear of the cabinet is designed to let air out. Might a top rear exhause fan fix this as well?