Headroom, and (if you're fond of bundling multiple channels of unshielded cables) crosstalk are the ONLY things compromised in balanced interfaces that don't drive symmetrical signals. I've had this argument a thousand times! When we proposed a change in the IEC's CMRR test (in IEC 60268-3) back in 2000, we got exactly this pushback, largely from Europeans who seemed to have an intellectual investment in the idea that equal-but-opposite signals are essential to noise rejection (as is wrongly taught in many textbooks as well). The revised standard, using a method I proposed, has an "informative annex" to explain that only the impedance balance matters in a balanced interface! In my seminars, I've offered $1,000 to anyone who can (using science, not screaming) prove that signal symmetry has anything whatsoever to do with noise rejection. Remember that the reason we use balanced interfaces in the first place is to reject noise (from ground-voltage differences between send and receive devices and/or for voltages induced in cables by electric or magnetic fields). You could make line drivers that deliver symmetrical signals on the two lines. doubling headroom and cancelling crosstalk, but it won't reject noise unless the impedances of the lines (with respect to "ground") are matched - and that includes driver, receiver, and the line itself since they're effectively paralleled. If you can visualize a balanced interface as a Wheatstone bridge, with each of the balanced lines one leg of the bridge, you'll see the relationships required to "null" the bridge (reject noise). For many engineers who attend my seminars, this is the "aha moment!" The same misconception about signal symmetry leads some to "fiddle" the matched pairs of resistors in a simple diff-amp line receiver, too. The misconception is very widespread
Impedance balanced but asymmetrical are not "illegitimate" - but they allow for very flexible interoperability in equipment that can't afford a transformer or a high-performance "cross-coupled" output stage like the THAT 1646. Inexpensive gear is still being made with balanced outputs that are simply two single-ended amplifiers - shorting the low-side output to ground will cause release of smoke at worst and system crosstalk issues at best. Balanced asymmetrical outputs prevent that. I'm a member of the AES standards group working on project X152, which is an effort to, at least, disclose on their data sheets just what kind of balanced output their equipment has. Currently, the user has to guess or experiment to, for example, figure out how to connect the balanced output to an unbalanced input.
And to Jen - while I applaud your preference for "proper" interfaces like transformers or well-designed circuits like THAT makes, the signal on a balanced line is not ground referenced, it's strictly differential. Look at the secondary of a transformer output - any voltage you see on one line will have only a parasitic relationship to ground - as anyone whose ever tried to use one line to feed an unbalanced input will quickly find out. The other end of the winding will have only some small capacitance between it an ground, making that unbalanced input get a signal that's being coupled through that tiny capacitance (i.e., no bass). In an ideal world, balanced lines would completely "float" with respect to ground. Thinking of a balanced line as two ground-referenced signals is what leads thinking down the rabbit hole!