Don't think this is going to be worth the effort. Given that an ATX PSU costs between 20 to 80 euro, depending on quality and power rating, they are effectively a consumable that is rarely worth repairing. And if you want to diagnose a faulty one, it is much simpler to just have a known good one and temporarily swap them - if the fault disappears, the supply has a problem, if not, it is something else. If it was the supply then you can cart the bad one out to your bench where you are much better equipped.
Also such analyzer will need a fast ADC to be able to measure ripple, the same for measuring any transient testing, together with a bunch of control electronics. And in order to be able to measure the full load capability, you need something to dump all that current into - either large resistors or a bank of very beefy mosfets, along with the required cooling. That's going to be big and expensive. Without testing the load a marginal supply with bad capacitors could still look fine if you only measure the ripple ...
I don't see how you want to integrate a tester like this to fit into a 5.25" drive way with all those cooling requirements and having to unplug the original load (motherboard, drives, etc.) in order to do any load testing on it anyway.