How much does volume matter when breaking in amps and cables?

Absolutely none at all. Zarathu is right. There may be some speakers that loosen up in the bass after a few hours but that is about it. This myth got started by dealers telling their customer who were not sure that they liked a new piece of equipment, "you just have to let it break in." In a few weeks they get used to the sound and everyone is happy but in reality nothing changed. This break-in myth is the ultimate BS of all BS. The manufacturers do not want to say anything against it because the they do not want to alienate potential customers plus they can always use the break-in excuse. In reality it is not your equipment breaking in, it is your brain breaking in.

Oh, which means in geoffkait's case I have no explanation.

Did you perform surgery on your own brain, Doc?

It doesn’t matter at all, as breaking in cables and amplifiers is a myth invented to reduce returns  

Cable break-in is primarily about the dielectric and you need to run a significant fraction of the insulation’s breakdown voltage to do a "true" burn-in.

So yes, running higher volume through your speaker cables will accelerate your break-in ... domestic issues notwithstanding ;-)

This is one sad reality of tonearm cables - that you’re running a fraction of a microvolt through them. For this reason, we burn-in the arm cables of tonearms before delivering them to our customers.

The less dielectric, the easier/quicker the burn-in, to the point where I’ve observed a total burn-in time of about 30 minutes for our litz interconnects with their cotton jackets.

On the other hand, a thick Teflon jacketed cable could take 400-500 hours.

Interestingly, I’ve found that there’s no relationship between the capacitance of the cable and break-in time.

Teflon for example, has lower capacitance than PVC, and yet PVC reaches its "final" state much more quickly.

Which cable/material you’ll prefer is up to you and your system as I’m just talking about burn-in time.

Thom @ Galibier Design