Since you asked
1) A transformer is a filter. Anything that is not an AC wave on the primary side is reduced on the secondary. Noise reduction can be up to 20 dB but , more often, between 6 to 12. Common mode noise rejection is typically 120dB and normal mode is 60 dB for an EI-type transformer. Toroidal transformers are more closely coupled and translate more noise. Voltage spike reduction by a factor of 8:1 is fairly typical. There do not reduce harmonics, by themselves, without some trickery. In fact, they are more efficient at 400 Hz. Power transformers are not wideband audio transformers.
2) A transformer can saturate for a number of reasons besides being overloaded. As little as a 10 mV DC offset on the line will compromise any transformer causing mechanical hum and severely reduced capacity. Ironically, the same DC is completely eliminated on the secondary side.
3) The electrical load (amplifier in this case) is dynamic and reactive, meaning it does not take a steady current and doesn't leave one either. High speed digital circuits can create a lot of noise, in which case an iso reduces noise from going back into the AC line. Capacitors charge and discharge in spikes. Diodes, rectifiers ...yada,yada. That is one reason for oversizing an xformer and in some cases even exceeding the 15A capacity of the house circuit. Look inside a Pass XA160, for a blatant example, and you'll see a 3KVA toroid for a 550W class A steady draw.
4) The xformer, itself, is an inductive and capacitive load. Normal efficiency is about 90 - 92% but the "exciting" current (into no load) is often 10 -15 % of the maximum rating. Powering up an xformer is a lot like starting an electric motor and can draw several times it's normal current momentarily.
5) There is no reason why an adequately designed and sized xformer would slow down reactions or cause dynamic compression. The power had to go through several transformers before it reached your house. Underestimating and using smaller, less expensive units is the main problem.
6) Question: Does reducing noise and distortion sound less dynamic?
7) Isolation and step-down transformers are much more common and integrated than most people realize in hospital/laboratory, industrial and commercial systems.
There is much more that I don't know about transformers than I do know and the more I learn, the more I realize my ignorance. They are completely predictable only in hindsight and a unique art and science.