If you’re talking about this article, then you’re taking situationally correct statements and applying them as absolutes … which is not what the article actually says.
Its statements are qualified with “may”, “in many cases”, “usually” and so on. And that’s with good reason … because they’re not universally true. It’s very much a simplification of the actual state of affairs and. Showing suitable measurement would be good as it’d put what they’re saying in proper context.
Yes, noise will typically increase if you just take a single-ended amplifier, pair it up with a second one, run the second amplifier inverted, and use that to drive your output (that’s all a balanced amplifier is). It’s almost always the case that that noise remains below the threshold of audibility.
Will distortion increase? Maybe. However, depending on the parameters of the design and it’s implementation, other distortion products (i.e. not simple noise) may well decrease as the amplifiers can be more easily made to operate within a sweet spot for bias and linearity as they only have to work half as hard for the same effective output level.
Damping factor halves … okay … technically … but is 0.2 ohms vs. 0.1 ohms really relevant into a 50 or 300 ohm load? Nope, not. really. It might be, at a stretch, into a super-sensitive, low-impedance IEM, but even the 8-9 ohm designs are still seeing a damping factor of several times the recommended 8-10x.
In many cases you can test if a specific amplifier is performing worse into your specific load, at your specific drive level, in single-ended vs. balanced configuration directly - by only driving one side of each channel and only taking output from that same side and measuring that.
But it’s not really surprising that a company that doesn’t produce balanced headphone outputs is going to put up an article that say’s they’re not always better.. (As it does NOT say they’re always worse).
Without specific examples and measurements, which would only be “objectively superior” for that case and not universally applicable, it’s just a position piece, not an engineering or scientific paper.
All that said …
You absolutely should worry more about pretty much every other aspect of an amplifier design, topology and implementation before you start worrying about whether it’s balanced or not. And there are plenty of single ended amplifiers that sound better than balanced ones.
There are, of course, definite disadvantages to a balanced amplifier … the biggest typically being value.
It will cost, generally, about twice as much on the BoM as a single ended version of the same amplifier. Though often it’s more because it as well as doubling up on PSU capacity and the number of amplifiers circuits it must provide, it’ll include additional circuitry to let single-ended sources drive the balanced amplifiers (which requires phase inverters or transformers), and to allow a balanced source to feed a single-ended output (which requires summers or transformers).
This tends to mean that if you spend $1,000 on a single-ended amplifier, it’ll be “better” than a balanced amplifier at the same price. And that’s often simply due to the balanced design not being able to use a design, or parts, that cost as much as the single-ended alternative as it needs twice as many of them.
Many tube amplifiers are designed in a way that does, indeed, increase harmonic distortion and, typically, they’ll exhibit higher noise than well-done solid-state designs. However, “many” and “typically” is not “all” and it is entirely possible to design and build a tube amplifier that measures as well as a solid-state device. It might cost more to do it depending on what bandwidth you need, but there’s nothing inherent to tubes vs. transistors that makes solid-state amps universally superior.
Proper application of the appropriate technology in a suitable design makes most of these “absolute” or “definitive” statements into what they really are … more “myths” and “beliefs”.
As with most things in life, the truth is almost always somewhere in the middle.