@dynamiclinearity I'm going with 'a fair amount'.
The venerable Dyanco ST70 has a damping factor of about 15. This does not change with a 4 Ohm load since you'd be using the 4 Ohm taps. It would be cut in half if you ran a 4 Ohm load on the 8 Ohm tap.
ElectroVoice made a number of tube amps (such as the A30) that had a damping factor of 15 back in the 1950s. It was EV and MacIntosh who came up with the idea of the amplifier being a Voltage source and the speakers being Voltage driven; this to enhance plug and play.
Prior to that speakers had adjustments on the back (midrange and tweeter level controls) to allow the speaker to be adjusted to the unknown output impedance of the amp.
The Mac MC275 had about 15:1. The Marantz 8b amplifier had a damping factor of 16:1. The famous Fisher SA100 was 20:1.
FWIW no speaker made needs a damping factor of over 20.