For measuring high voltages / mains safely, you'd need a CAT rated differential probe though.
No, you don't need a differential probe. A single-ended probe designed for floating measurements will also work. It's not like the reference level is moving much relative to earth. If you read the manual for high voltage differential probes, they have statements like "make sure the oscilloscope is grounded" or "These probes are designed for use with oscilloscopes that have a common terminal at GROUND POTENTIAL". So I'd say a single-ended probe for floating measurements is a better choice for a battery-powered scope with isolated inputs (the only type of battery-powered scope I'd use on mains). Either that, or use a grounded scope with a high voltage differential scope.
You are confusing a few things here.
1) There is no such thing as a single ended probe for floating measurements. You always need to clip the reference / ground side of a probe somewhere in order to measure a voltage difference between two points.
2) An oscilloscope with isolated inputs is functionally comparable to using a differential probe + normal oscilloscope. Only difference is that the isolation happens inside or outside the oscilloscope
3) Needing grounding is a safety issue. If the differential probe breaks or (more likely) the user makes an error, a non-isolated oscilloscope which is floated can present dangerous voltages to the user.
So in the end the choice is between paying more for an oscilloscope with floating inputs compared to using an external isolation device like a differential probe combined with an oscilloscope. What is most economic and desirable, depends on the requirements. Handheld oscilloscopes with isolated inputs typically have less features as they are more geared towards simple field measurements.