What are the specific scenarios that an isolation transformer is useful for avoiding?
It sounds like there's some sense that you could in theory poke at various components while the device is powered on and as long as you only touched in single places and didn't accidentally bridge circuits you would be safe, but this doesn't sound intuitive to me. I mean, I'm in danger normally of shocks towards ground even with shoes on, aren't I?


That's the main reason.  A normal supply has a grounded neutral.  If you accidentally touch a live wire, you provide a path for the current through the earth and back to the neutral.

With an isolating transformer, the secondary of the transformer has no connection to ground.  Even if you touch a live wire, there's no path for the current.

But the isolation transformer does nothing to save you if you accidentally touch the live and neutral at the same time.