I was running one of my projects from a "switching power supply". Many now are of this type, btw. I believe that it means that the power supply will sense the load; if it's below a certain current it will switch off. In some cases, it's necessary to add a resistor in parallel to the load to slightly increase the load so that the power supply doesn't switch off. My situation resulted in the input power cycling ON/OFF, for what it's worth. It's possible that this could be related to what you were seeing there.
I'm confused. You indicated that you're using an ATX power supply and then you suggest that it's advertised to be 5V @ 2.5A so that doesn't make sense to me. A typical ATX power supply is silvery-looking and boxy and includes several sets of wiring harnesses from it; a typical Raspberry power adapter is a.k.a. a "wall wart", has prongs and a black plastic covering which encloses a transformer, some coils and capacitors mainly. It only has the one connection either as a USB Type A receptacle or as a micro USB plug.
I suppose I shouldn't be too surprised at the numbers you're throwing with respect to power. Later, you should also profile what it looks like when you've added a webcam and further, when you're streaming the output back to your workstation. The Raspi3 has four cores and there are moments when OctoPrint uses all of them simultaneously. Personally, I've found that deleting a large timelapse file seems to be unnecessarily hungry for processing for some unknown reason. Give yourself some wiggle room. Note also that percentage of time uploading/downloading via wi-fi can also change those numbers as well as writing to the microSD. You might try using
scp to push a large temporary file to the microSD from your workstation and see what the power requirements look like then.
That said, the topic of USB power toggling has been discussed before on here.