To be clear, gravitational waves follow the same inverse square law as EM radiation, in terms of power. This is after all just a statement of conservation of en

To be clear, gravitational waves follow the same inverse square law as EM radiation, in terms of power. This is after all just a statement of conservation of energy. The linear drop-off you're referring to is when we look at it in terms of field strength (in this case the spacetime strain). Since power is proportional to field squared, this implies a linear drop-off in the field. It just so happens that for GWs it's easier to detect the field, whereas for (most) EM radiation it's easier to detect power. There are field-detection methods for EM radiation as well, which are useful for weak signals. Homodyne and heterodyne detection are good examples.