Q:

Image rejection

Google is not helping me on this one.
I get that image rejection is important when demodulating an RF to an IF frequency.
But what about when demodulating an RF directly to an wideband signal?
I mean, then the image would be placed in the negative frequency domain, exactly as it was when the signal was generated in the transmitter.
Is it because of wasted energy of transmitting both the signal+image?

A:

Yes, image rejection is a potential concern anytime you have a mixer, including in a "product detector" where you "demodulate" by mixing to baseband.
Such a mixer producing a single output will combine the positive and negative frequencies in a way which cannot be distinguished - a classic example would be tuning a steady carrier (or a modulated one, as in morse code) using a direct conversion receiver / product detector mixing to audio.  As the local oscillator nears the transmit frequency, the audio tone will fall through the audio bandwidth towards zero.  As the LO frequency passes the audio the transmit frequency, the audio tone starts rising in frequency again.  With a single output and no other reference it is not possible to distinguish positive and negative frequencies from each other.  An input spectrum which contains both could therefore become quite confused.
An alternative approach is IQ mixing.  Here two local oscillator signals in quadrature are produced (ie, sine and cosine) and mixed with the same input signal to produce two outputs.  The phase relationship of the outputs can then be examined to determine if (a given component of) the signal has positive or negative frequency.  Many baseband signal processing algorithms and modulators/demodulators operate on IQ signals.
An additional option is to shift one of the I or Q signals by 90 degrees and subtract them.  This will destructively cancel either the positive or negative frequencies, forming what is known as an Image Reject Mixer.  However, generating a precise 90-degree phase shift can be tricky to do, especially over a wide bandwidth.  The merits of doing this, vs using filters to eliminate one of the image possibilities depend on the frequency and bandwidth of the signals to be processed, performance requirements (allowable phase distortion and image leak through) and type of technology available for implementation (ie, DSP vs RLC, crystal, mechanical, SAW, cavity, etc filters)

