Power factor and recitfiers
It's not that 'a lot of commercial transformers like sinusoid'. It's simply that every transformer has issues (usually heating or vibration) with frequencies over the one it is designed for. So a 50Hz transformer would have to handle 100Hz, 150Hz, 200Hz and so on.
The EN 61xxx standard (in EU, the US would probably have some FCC related stuff) mandate a limit on the shape of the current from the equipment powered by mains (harmonic distortion testing).
Since the Fourier theorem holds for periodic signals, there is a limit on the upper harmonics of the current signal: with a purely sinusoidal current the upper harmonics would be 0, but even a rectifier bridge will alter that (since the diodes conducts only at 0.7V).
During the test you literally do a fast fourier transform of the current signal, with some good precision (IIRC you need at least 16 bit of resolution) and compare the upper harmonics with the fundamental and the standard limits: it's a pass/fail process. Buy the standard or look around for the relevant figures.
The power factor is strictly related and is a summarization of the harmonic test: it is in fact equal to the cos-phi of linear reactive loads, and some nasty integral in the general form (the definition is easily found on internet). So a bad power factor not necessarily indicates harmonic distortion (if it's only due to reactive load); severe harmonic distortion however causes a bad power factor (due to the way the PF is calculated). An reactive-only PF is not strictly bad for the transformer, is more an efficiency issue for the transmission network (reflected power causes unnecessary heating), and is handled by other kinds of standards.
Diode rectifiers are somewhat bad, but most of the time they pass the test; the worst load is a phase controlled load (like TRIAC dimmers) since the straight current edge has a huge harmonic content.
Switched regulators fall in between: they pull current in pulses of about 10-250kHz and that makes a bad PF. For small power supplies you simply put an inductor on the input of the supply, to smooth the current (old ATX supplies actually used a fluorescent tube ballast coil for that!). More powerful or better one use an active PFC circuitry which is quite complex to explain but can reach even PF 0.99