Suppose you only work on low voltage circuits (e.g. 5V, 12V, 24V), and you use a power supply with isolated outputs.
As indicated above, it is no issue to connect the ground clip of the probe with any point in the circuit, it just makes that potential level your ground from then on. That's clear.
The case of the scope could become 5V, 12V, 24V. Not pleasant to touch, but not harmful.
But I guess it still makes sense to have a differential probe anyhow, as you can still short your scope when you would connect the tip of the probe with the ground clip (not being actual ground, but having a higher potential level).
The differential probe can not be shorted, it only measures the difference between two potential levels. The probe of the scope can be shorted, when clip and tip have different voltage levels and no resistor is in between. Is that correct summary?
I told these observations to a friend with a 4 channel scope. He wondered why the manufacturers of scopes not just build this in as standard. This would make it cheaper as well, when it becomes mass production (a la Rigol). As there is no such scope, he is planning to buy 4 differential probes at once to avoid all the discussions and worries at once. Maybe Pintek offers a discount when buying DP-30HS differential probes in bulk