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Copper pour is especially important for GND, since it enables every signal to have a close by return current (minimizing loop area and thereby EMI etc.)
When using copper pour for other signals such as power: in principle this can be done and sometimes this is even advisable, since esp. when taking care that the layer stack is such that e.g. the power plane is closely spaced on top of the power plane, that you'd have distributed capacitance of VDD-GND which may be beneficial in some circumstances. It is also convenient for routing, since you can 'pick off' the power supply at any desired point.
However, there are some things to take into account when using copper pour for power planes: when drawing the boundaries of the power plane, take care that the area doesn't get close to other areas where there may be some unwanted coupling. For instance, prevent a digital VDD plane to come close to a sensitive analog circuit and vice-versa.
In general, I personally like to prevent using power planes. For sensitive circuits I then use star connections. When manually routing the power connections, I am in full control of what parts gets its power how and this lets me think about what would be best in terms of EMI. When using power planes, this would be more 'automatic', with some chances of unforeseen issues.
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