A ground plain obviously reduces the usage of etchant when producing a pcb. I have always thought they were applicable only to HF circuitry but is there any reason not to use a ground plane with LF or DC circuits?
For low frequencies, ground planes are not necessary.
However, with some I.C.s having a ground plane redudces possibly instabilities caused by circuit layout and high input impedances.
It does offer some shielding, remember the old days when you might pickup a radio station on an amplifier.
Less etching is a good thing too.
With Arduino stuff it would be recommended to use one along with proper decoupling techniques.
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