If I had to think of the worst thing I might add to a power amplifier, an output transformer would be right up there - yet the vast majority of tube power amplifiers sport them.
Tube amps interface their output stage with your loudspeakers through a matching transformer, not because it sounds better but because they need to. A few tube amps have gotten away from this output coupling device and they are called OTL, short for Output Transformerless amplifiers, but they are the exception not the rule.
Loudspeakers are very low impedance devices, ranging from 16 Ohms down to under 1 Ohm depending on the design. Tube power amplifiers are relatively high output impedance devices, ranging from a low of about 600 Ohms to a high of many thousands of Ohms. That's not a great match, hence the need for a matching power transformer - the quality of which has a great deal to do with the sound quality of the amp.
What a loudspeaker wants is to be whipped into shape and commanded to do what it's told - that job is well suited to a device that has an output impedance far lower than the lowest the speaker will go. A properly designed solid state amplifier has an output impedance that is well below 1/100th of an Ohm - perfect for bullying a loudspeaker into doing its bidding.
And here's another point I would like to make - when your loudspeaker manufacturer tells you their speaker is a 4 Ohm or 8 Ohm version, rarely is that true for music - because that impedance figure is frequency dependent. The input impedance of a speaker can be all over the map depending on the design and music being played.
Some of you may have been around long enough to remember the Infinity Kappa series or the Apogee ribbons - these hogs dropped down to well below an Ohm - and as an amplifier manufacturer for many years I can tell you I lost quite a number of output stages to these speakers.
Interestingly enough tubes were valued to drive both the Kappas and the Apogees because of their output transformers - which "didn't mind" those wild drops in impedance that were shutting down and even killing solid state amps of the day. However, while they "didn't mind" the impedance drops they also didn't produce anything close to a flat response at those low impedances either. So while a solid state amp was doing its best to keep up with the speaker load - admirably delivering the proper musical signal until it either quit or died - the tube amps just gave up and ignored the musical demands when the going got tough.
This "glossing over" of bass frequencies helped give rise to the term "tubey sounding bass" where you never really got good bass, it was just kind of tubby, loose and (shudder) warm sounding. Oatmeal.
Much of the merriment amongst tube amp owners of the day was in response toinadequaciesof the tube amp's output transformers and the crazy impedance demands of some loudspeakers of the day. Today's loudspeakers are much better behaved and get along with the output transformers of tubes much better, but their issues will never go away.