I do care, but only if you use Chain-L. To properly lube a chain it has to be dry inside, so the newly applied product can wick into the chain where it needs to be. The most common chain cleaning error is failure to dry completely, especially if using water based cleaners which can be retained inside the chain by capillary action for a long time. Think about water that seeped under a glass table top for comparison.

If the chain isn't dry added lubricant will sit on the outside and be wiped off before it can do any good. It's like trying to wipe up a spill with an already soggy towel.

I don't care how people clean or lube their chains, though I'm obviously happier if they use my stuff. But I really do care how Chain-L users clean their chains, because poor technique yields poor results which reflect poorly on my product and me.