An amplifier having "constant power" aka "constant wattage" characteristics will, for a given input voltage, tend to deliver less output voltage at frequencies for which speaker impedance is low, and more output voltage at frequencies for which speaker impedance is high. That will result in loosely approximating delivery of constant power into those varying impedances. Most tube amps fall into that category, to a loose approximation. How loose that approximation is will depend on both the output impedance of the particular amplifier (which varies widely among different tube amps), and on how the impedance of the particular speaker varies over the frequency range.@almarg Just as a bit of clarification on this bit: any tube amp can be made to act as a voltage source if you can add enough voltage feedback. If the amp is zero feedback it will behave more like a power source. Further muddying the waters is the simple fact that just because an amp doesn't double power as impedance is halved does not mean that it can't behave with a constant voltage characteristic. Many tube amps do exactly that.
In the 1950s before the idea of voltage driven speakers caught on, it was seen as a good thing to make sure that the amp had low distortion as well as the correct damping factor for a given speaker. Now some open baffle speakers need a damping factor of only 1:10 and you did read that correctly: where the amp has 10x the output impedance as opposed to the loudspeaker. OTOH some speakers do need 20:1 to sound right.
To allow this to occur, in the 1950s a number of amps were made with a 'Damping Control' which balanced voltage feedback against current feedback. So at one extreme the amp behaved with constant voltage; at the other with constant current, and in the middle where the voltage and current feedback were in equilibrium, constant power. BTW its worthy of note that this idea has nothing to do with solid state vs tubes.
IME/IMO, while the Voltage Paradigm has taken over decades ago, the simple fact is that there are speakers out there that don't and **can't** work under the voltage rules- specifically ESLs, a number of magnetic planars, a good number of horns, 'full range' drivers and certain box speakers that designers noticed that they sound better with tubes than solid state... I think the damping control isn't a bad idea at all; if you want plug and play, the damping control is more likely to do the job for you.