Is subtraction a common method for efficient filtering?
You are right about the importance of the phase.

Subtraction in the time domain is equivalent to subtraction in the frequency domain. If the frequency domain phase at some frequency is not equal between the complex number being subtracted and the complex number subtracting, even if their magnitudes are the same, the result will be non-zero:


Figure 1. Subtraction of complex numbers of equal magnitude does not always result in a zero. The calculation is black = red - blue.

If the black dot represents the combined frequency response for a system output = input - filtered input at a frequency that you intend to be part of a stop band, you must ensure that the filter is zero-phase. Or if the filter is linear-phase and has in its impulse response a center of symmetry at some time, you must delay the copy of the input by the same amount of time before subtraction. This will not work with efficient infinite impulse response (IIR) filters because of their non-linear phase.