The idea comes up from time to time. Everyone should do their own assessment of the kinds of events/risks that they are preparing for. To me, the one big drawback of any sort of continously refreshed stored water supply is that your entire water supply--or a big chunk of it--can be contaminated before anyone realizes that there might be a problem with the incoming water supply.

Just this past week, Gov. Schwarzenegger declared a water emergency in Barstow, California due to perchlorate contamination in the tap water, and New Orleans also declared a boil order. If no one is sure of when the contamination started, then I think most of us would at least be suspicious of that stored water. With the infamous Milkwakee crypto incident with their municipal water, the authorities did not realize there was a problem for weeks.

I think a storage system that is directly hooked up to the plumbing is very convenient, however, I don't think I would personally have it continously circulating water due to the contamination risk. Instead, I would manually refresh the water on some schedule. I assume that it might be as easy as twisting some bypass valve to redirect the incoming water through your in-line water storage for a while to refresh them, and then repeating again in 6 months or whatever interval you choose.

There's nothing wrong with "old" water that was stored properly--even very old water--except that it will be flat and possibly pick up a certain taste from whatever container it is stored in.