For THD+N, you essentially measure all power (harmonics, spurs, noise, etc.)
To me it sounds more plausible to measure everything than "only" the harmonics - Or do I have a thinking error?
I guess so…
Of course it used to be a lot easier to measure THD+N, as it just required an RMS voltmeter and a notch filter. This is how the traditional distortion meters work. No way to measure (and calculate!) THD without a spectrum analyzer.
But just because something was much easier to accomplish in the past, it is not automatically more plausible as well. You might think so as an end user ("I don't care what it is, it just doesn't belong there!"), but even as an end user you are affected differently by the different unwanted signals.
Consider the most popular area where distortion is a big thing: Audio. So you have, say, -50 dBc THD+N and you think this is fairly bad and it does not matter where all the unwanted signals stem from. But:
• If it's pure noise, then your signal is essentially distortion-free but the signal to noise ratio is just 50 dB. Some folks won't even notice that noise, at least not with low dynamic pop/rock music…
• If it's pure harmonics, then you might notice it because of a slightly altered sound. If the harmonics happen to be predominately even numbered, then the audiophools will rave about the "warm and fuzzy" sound as they are used to it from their single ended tube amplifiers - using a (highly linear) light bulb as a pullup resistor
• If it's only spurs, then it will sound rather disturbing and folks who wouldn't have taken notice in one of the two previous cases might start to complain all of a sudden.
So even the end user would prefer separate specifications for THD, S/N and spurs.
For the designer of such gear it's of course all the more important to know where the unwanted signals come from. Needless to say that the investigation as well as the final countermeasures look very different for the three different types of unwanted signals mentioned before.