That makes sense, but using the same water for weeks at a time seems a bit disgusting to me. Even if it is boiled quite often.
Sorry I wasn't able to edit it.
You keep it at a slow boil, and properly salted, all day long. If you're using it more than one day, you'd probably want to keep it hot overnight, like "perpetual stews", but I can't attest to how common this is, especially in restaurants that aren't constantly plating pasta.
You can manage it as a batch process, throwing the water out when it gets too starchy, but doing this unaided leaves you unable to use the water as emulsifier at the start of the cycle. You could also do it as a perpetual process by pouring some off the top and refreshing with clean water.
And what's to wash? You don't wash food after cooking, and pasta is like bread -- it certainly doesn't need washing beforehand either. It's just flour and some other ingredients.
It's not like vegetables where you need to wash off dirt, pesticides, etc. Or meat where you wash off bacteria. Those aren't issues with pasta.
Just from a food safety perspective I'm not sure it's legal to reuse across days, given that it's going to take all night to cool, only just in time to be reheated again.
If there was a way to get rid of the insect eggs people would presumably want to do it too, but iirc they're just too small to filter out.