To answer the question why are the constants so often omitted, I would like to supplement QtizedQ's point (that the constants are of less interest because often relative intensity ratios are used). Focusing on proportionality rather than a strict equation with constants also leaves "amplitude" ambiguous, where it could refer to either the electric field or the magnetic field. Because (in a vacuum) the amplitudes of both perpendicular fields of the electromagnetic wave are proportional, we can say the intensity is proportional to both the electric field and the magnetic field (by different constants). The consequence of the proportionality between the two amplitudes is that when discussing electromagnetic radiation qualitatively, it doesn't matter which amplitude we are talking about - we can simply say "intensity is proportional to the amplitude". In fact, this statement is true of waves in general (both transverse like light and longitudinal like sound). Different physical wave systems will have different constants, and there are a variety of quadratic equations between intensity and amplitude, but if we ignore the constants, we can make a broad statement that is true for waves in general: $I \propto A^2$.

The proportionality form is more general, more convenient, and perhaps even pedagogically more tractable.