Forgive my ignorance, but wouldn't this essentially be the same as plugging the amp into a non-grounded outlet?
No because neutral and ground are tied together in the panel… sometimes. You’re isolating neutral, ground, and hot all three for your own safety
when your test equipment is also referenced to neutral and ground.
Here’s a good video as to why it’s for your safety.
Edit:
Also let me make it clear that you never want to just plug a device into the wall without a ground reference regardless of whether you’re testing it or not. What that does is make
you the reference to ground which can be absolutely deadly. I don’t have to link the countless people dying from touching electrically hot microphones or electrically hot stages but I will if I have to for your safety.
An isolation transformer prevents you from being the return path of a ground loop that involves your DUT and it’s important when using measurement equipment because the probe grounds on an o scope are not isolated and attach to chassis ground directly. So if you touch a ground probe to a ground that isn’t ground, and your DUT isn’t isolated, you very well could be the return path.
The reason it’s not an issue with battery equipment is that they’re floating as they are, so it’s not an issue or a concern for your safety. Additionally, don’t isolate the oscilloscope, always the DUT.