Did you look at this case? https://www.amazon.com/Argon-Raspberry-Heatsink-Supports-Accessible/dp/B07WMG27T7/ref=sr_1_2?dchild=1&keywords=pi4+argon&qid=1592447696&sr=8-2
I have it and am a fan. The whole thing is a heat-sink except for the very bottom piece, which I was a little confused why they made that part plastic. The lid would probably slide right over the POE hat.... Probably, 99% sure just looking at the photo of the hat and holding the case.
If you have stand off's and are handy with a soldering iron you could potentially modify the fan hat attachment for the case to fit the POE hat if you really needed the cooling but the lid definitely would not fit any more
I haven't seen that one, looks nice but no option for the fan.
A lot of these "metal cases that act as heat sinks" don't really do all that much. Especially if you use the thermal compound included and not real thermal paste.
It seems the later firmware does a good job reducing the thermal problems with the Pi 4. I am going to do some testing when I get my Pi 4's in, I am still using Pi 3's and Zeros. I'm still going to go with a fan case and can run the fan in quiet mode if cooling isn't a big concern (there are two pins you can choose from when attaching a fan to decide if it is in quiet mode or full-speed mode).