The biggest issue with input/output impedance is the change in frequency
response. This is especially bad with tube pres as they usually have a
high output impedance. Driving a low impedance input amp can affect the
overall response and deviate from ideal. With purist tube pre's even the
volume control setting can affect things because they lack additional
buffer stages that would prevent this.
This is mostly misleading or outright false.
Output impedance **might** affect frequency response (in some cases, certainly not if the output is direct-coupled) but also affects distortion.
Tube preamps do not necessarily have high output impedance. That depends a lot on the design of the circuit! If it employs feedback, its output impedance will be fairly low and driving a 10K impedance should be no worries- check with the manufacturer (our preamps don't employ feedback and 600 ohms or less is no worries)! In a purist tube preamp, the volume control won't affect things (other than volume) despite there being no buffer; its all about how well the design is executed!
As an example, we make two tube preamps that have balanced outputs (and were the first in the high end audio world with such) and the load that they can drive makes no difference- the frequency response is flat, owing to a direct-coupled output. They also support driving 600 ohms as they were intended to support the old school balanced standard. Yet because they lack loop negative feedback, their output impedance is relatively high (compared to most solid state preamps), yet their distortion is very low driving any amplifier made with a balanced input. I've used our MP-1 to drive loudspeakers directly; how many solid state preamps can do that?
Just sayin'.
