I don't think the amount of volume is going to make any significant amount of difference. I have burned in many cables, including speaker, at just low to moderate volumes. Consider this. Digital type cables (including spdif and hdmi) will typically only push 0.5 to 0.6 volts on the data conductors. However, analog audio can be up to 1.4 to 2 volts. In either case, both cables can be burned in with similar timelines. Speaker cables will see significantly higher amounts of voltage (such as 5-50 volts or more, depending). I think it's more important to send an amount of charge/discharge activity down the wire to help break it in.
How much does volume matter when breaking in amps and cables?
I'm not here to debate break-in. I generally leave new amps, components, and new cables playing low volume for a for long periods to start the break in process. Just curious how much does volume play a role in breaking in such. I get that speakers probably need pretty good amounts to push drivers, but what about other components?