Why does this not work for all transfer functions?
Equating real with imaginery locates the turning frequencies of the system and this hints at the poles. In the example of an RL high pass filter but with an extra resistor in series with the inductor, there are two frequencies of interest. 

The first (lower) is when the inductor's impedance equals that of R2 (the extra resistor in series with L) and this marks the point at which output starts to rise with frequency. 

The 2nd frequency of interest is equivalent to the original -3 dB point where the |reactance| of L equals that of R1.

Now, when you do the math and equate real and imaginery, sure you can solve it - it's a bit of a complicated quadratic and, of course with a quadratic, it produces two values for \$\omega\$ and these are the turning frequencies.

So, what is the problem?