ALWAYS be careful of any capacitors as they can give a deadly kick. Make sure everything is fully discharged before you open it up and start sticking your saw and screwdriver in there....
As in: "If the pc case is good enough enclosure and is not secured with thumbscrews, why do you need a separate enclosure for the psu?"
Because of the many high voltage sources both under the pcb, and over including one or more of the heatsinks! The pc would no longer be safe to fiddle in, whilst off or on
As long as you can keep enough airflow moving over the heatsinks i don't see why not. Do you have access to a IR heat meter? That way you can check temps with the 120mm and then after to see if they have risen too much.
Some great suggestions here, thanks everyone. I am a big stickler for keeping everything in the case. Even externally mounted reservoirs make me cringe I don't want to give away anything yet, but the design calls for a slim case, but it has room for the other dimensions of the PSU to grow. One thing I had been thinking about was that PSUs are the size they are because they are a standard. This is no call to change the ATX spec.
Just for the record, I had already mentioned that. The smaller size (server) PSU standards exist for a reason too, and I honestly think a 1u or 2u PSU would be better than beginning to hack up a full ATX one. Before you think any further about not housing the PSU in a separate unit within the PC, just don't. Ever. MV has already mentioned it, but I'll re-iterate it. The cover/shell on a PSU isn't there for show and it's not even only there for safety - it's an electrical shield and a proper ground, and if you remove it entirely you will have all sorts of issues with your PC. Again, I am speaking from experience here... I've been modding PSUs for a long time and have carried out some experimental mods on my own hardware to test theories like a cover-less PSU which is cooled by the PCs airflow and whilst they all worked in some capacity, some of them were far from ideal.
Then I misread your OP, apologies. I have NO intention of not housing the PSU in its own case. This whole concept is in flux because I don't even have a finalized design for the main case. I understand about EM problems (though only the basics) and respect your history and knowledge of this type of mod. That said, I see no reason not to push the boundaries a little, should I need to.