If you use the transformer to boost a voltage gain and a buffer to boost a current gain you may make your buffer with a voltage gain = 10 eliminating one expensive and distorting part.
Completely different story would be if you have input resistance after the transformer equal to output impedance of a source multiplied by a resistive ratio of the transformer, for example to feed 600 Ohm signal to input of a tube amplifier.
Transformer on input is needed to isolate input from in-phase noises, it is the main purpose of it. Speaking of colorations, everything will add colors, either instrumental amp, or a transformer, but if to choose one evil from 2 some people choose the one that looks more natural, i'e' which distortions sound closer to distortions of a sound in the real (not electrical) world. It may be a transformer.
The second purpose of the transformer is to match impedances, i.e. to pass the signal with the less as possible power loss. I do not know where 600 Ohm standard come from; air lines have higher impedance, cables have lower impedance, but we have to live with standards and match the gear to each other according to them.
If input impedance of amplifier is higher the ratio of the transformer must be higher, it means more voltage / less current is needed from it's secondary winding. The higher is bigger until input capacitance start roll off highs too much, or the transformer becomes expensive out of the desired range.
In case of transistor inputs the story is a bit different; they start produce more noise when source impedance is higher than certain level, or lover than some other level. It is always an equilibrium to get the better ratio between un-noised and un-distorted signal (of course, noises and distortions always present, the difference is in their amount).
Output transformer again is needed for couple of purposes.
A first, an impedance match to save the power and get wider dynamic range and lower distortions.
And second, again to help the next peace of equipment and minimize noises on it's input from ground loops and electromagnetic waves on cables.
If output impedance of your amp is good without the transformer you do not need it. But if you are going to connect it to the symmetrical input of the next device it is better to make it symmetrical.
And again, you may use an active phase splitter, or a transformer. Both will add coloration, the question is which colorations do you prefer.