Q: Why do I have to match speakers to the output impedance of the amp?
A: You'll get the most power out of the amp if the load is matched.
Q:Will it hurt my amp/output transformer/tubes to use a mismatched speaker load?
Simple A: Within reason, no.
Say for example you have two eight ohm speakers, and you want to hook them up to an amp with 4, 8, and 16 ohm taps. How do you hook them up?
For most power out, put them in series and tie them to the 16 ohm tap, or parallel them and tie the pair to the 4 ohm load.
For tone? Try it several different ways and see which you like best. "Tone" is not a single valued quantity, either, and in fact depends hugely on the person listening. That variation in impedance versus frequency and the variation in output power versus impedance and the variation in impedance with loading conspire to make the audio response curves a broad hump with ragged, humped ends, and those humps and dips are what makes for the "tone" you hear and interpret. Will you hurt the transformer if you parallel them to four ohms and hook them to the 8 ohm tap? Almost certainly not. If you parallel them and hook them to the 16 ohm tap? Extremely unlikely. In fact, you probably won't hurt the transformer if you short the outputs. If you series them and hook them to the 8 ohm or 4 ohm tap? Unlikely - however... the thing you CAN do to hurt a tube output transformer is to put too high an ohmage load on it. If you open the outputs, the energy that gets stored in the magnetic core has nowhere to go if there is a sudden discontinuity in the drive, and acts like a discharging inductor. This can generate voltage spikes that can punch through the insulation inside the transformer and short the windings. I would not go above double the rated load on any tap. And NEVER open circuit the output of a tube amp - it can fry the transformer in a couple of ways.
Extended A: It's almost never low impedance that kills an OT, it's too high an impedance.
The power tubes simply refuse to put out all that much more current with a lower-impedance load, so death by overheating with a too-low load is all but impossible - not totally out of the question but extremely unlikely. The power tubes simply get into a loading range where their output power goes down from the mismatched load. At 2:1 lower-than-matched load is not unreasonable at all.
If you do too high a load, the power tubes still limit what they put out, but a second order effect becomes important.
There is magnetic leakage from primary to secondary and between both half-primaries to each other. When the current in the primary is driven to be discontinuous, you get inductive kickback from the leakage inductances in the form of a voltage spike.
This voltage spike can punch through insulation or flash over sockets, and the spike is sitting on top of B+, so it's got a head start for a flashover to ground. If the punchthrough was one time, it wouldn't be a problem, but the burning residues inside the transformer make punchthrough easier at the same point on the next cycle, and eventually erode the insulation to make a conductive path between layers. The sound goes south, and with an intermittent short you can get a permanent short, or the wire can burn though to give you an open there, and now you have a dead transformer.
So how much loading is too high? For a well designed (equals interleaved, tightly coupled, low leakage inductances, like a fine, high quality hifi) OT, you can easily withstand a 2:1 mismatch high.
For a poorly designed (high leakage, poor coupling, not well insulated or potted) transformer, 2:1 may well be marginal. Worse, if you have an intermittent contact in the path to the speaker, you will introduce transients that are sharper and hence cause higher voltages. In that light, the speaker impedance selector switch could kill OT's if two ways - if it's a break befor make, the transients cause punch through; if it's a make before break, the OT is intermittently shorted and the higher currents cause burns on the switch that eventually make it into a break before make. Turning the speaker impedance selector with an amp running is something I would not chance, not once.
For why Marshalls are extra sensitive, could be the transformer design, could be that selector switch. I personally would not worry too much about a 2:1 mismatch too low, but I might not do a mismatch high on Marshalls with the observed data that they are not all that sturdy under that load. In that light, pulling two tubes and leaving the impedance switch alone might not be too bad, as the remaining tubes are running into a too-low rather than too-high load.
