Technically, you should always provide a load that is recommended by the manufacturer of the amp. The designer of the amp chose a particular output device (tube) and specified all of the operating voltages for the output stage so the tube would work at its optimum efficiency while delivering maximum power to the load with minimum distortion. Ok, so let's discuss the problems associated with mismatches. When you use a load that is lower than the intended load, the output has to drive the load (speaker) with more current because it is a lower impedance than is expected. [...]
As the current draw in the secondary increases, the primary has a more difficult time transferring the signal to the secondary, so the secondary signal to the load gets squashed, or 'soft-clipped'. This soft clipping is called regulation. While regulation is desireable in a power supply, it is undesireable in a transformer. In other words, in a power supply, if the input voltage or the output load current changes, we don't want the output voltage to change. In a transformer, we want the output voltage to follow the input voltage and not regulate at all. [...]
OK, on to mismatching the other way. A speaker is a current operated device in that it responds to the current through it to generate a magnetic field that works against the magnetic field of the speaker magnet to make the cone move in and out. Thinking in very short amounts of time, when the output charges up the voice coil with current, then the signal goes away or gets reduced, the cone system moves the voice coil back to its home or resting position. As it is moving back, it generates a voltage that is fed back up the line into the transformer and appears in the output circuit of the amp. This generated voltage is often referred to as flyback voltage, because we are charging up an inductor, then when we disconnect or stop charging the inductor, the magnetic field in the inductor collapses and induces this big voltage into itself. This big voltage then 'flies back' to the source of the charging current. [...] The bottom line is that the voltage fed back to the output circuit is oftentimes much higher than the voltage that was used to drive or charge up the voice coil initially. This voltage gets transformed up by the turns ratio of the output transformer, and in many cases can be over 1,000 volts. What happens then is that arcing can occur between the pins on the output tube socket. Once this has occured, a carbon path forms on the tube socket between the pins. The carbon path allows a steady current to flow between the pins and eventually burns up the socket due to the heat that is generated.