What are some of the reasons why DC offset is considered undesirable for a timeseries signal other than wastage of power during transmission ? Specifically, How does it cause spectral leakage and out of band emissions ?
In a mathematical sense it doesn't but (almost) any nonlinear interaction, say modulation or demodulation, will cause additional signals, leakage/out of band, signals. The point is that when you do the evaluation you must include the modulator or demodulator; as well as things like transformers which will be biased off center and thus generate extra distortion. It's the non-linearities in the overall signall path that induce extra signals. By definition of the Fourier/Laplace transform superposition and linearity properties a linear system will not generate extra signals.
A signal with a DC-offset does not have a zero-mean. In audio & statistical signal-processing for example, many analysis and effect-processing algorithms make assumptions that the signal is zero-mean. A DC-offset-remover is a common pre-processing step, to ensure the correctness of algorithms further along in an effect chain.