So you want on schematic view something similar to the sticky setting for a board in the pcb view. A blank (or outline only) container part on schematic view that constrains the layout of other parts (but not wires) placed on (inside) it.
Fritzing does not have any functionality like that. It does allow multiple parts to be moved around together, if they are all selected. Either by a box drag select, or by individual multi-select and unselect.
For this particular case, I would just use GND and Power (V++) parts to tag the inputs and outputs, then use those where needed, instead of having the ground and power wires. That would separate (no connecting wires) the block from the rest of the circuit, making it very easy to drag select, and move around as a single unit.
Really what you want to do, is to turn a section of the schematic into a new (temporary) part. Your example looks like it acts like a 3 terminal fixed voltage regulator (with LED power indicator). So (functionally) it could be replaced by that part in the schematic. Which is what you want it to act like on the schematic, but keep the internal details visible.
An example could be a schematic with the components and internal connections for an UNO board, that is then “locked”, and acts (externally) just like one of the existing uno parts. It would get even closer to that, if the connectors could also be locked, to limit which were available to connect to from outside of the block.
I can see plenty of places to use that feature, but suspect that implementation would not be easy. Going that direction would probably end up merging the parts editor functionality into the main application. The basic ‘sticky block’ would be simpler, but still need some time developing the code.