I don't think that too many sailors drink from their water tanks unless they have to.
But using bottled water to flush your toilet? That sounds like a PITA, & you better have a lot of bottles lying around if its more than just yourself on board. I have a family of 4 & usually friends too, so that's just not gonna cut it. A lot of us freeze water bottles to bring on board, so that's not new news, but carrying all of your water on board is not very practical. Why not clean out your water tanks properly & at least use it for cleaning & flushing as it was designed? On our boat the sink is plumbed to drain into the head, so soapy water runs through the head helping to clean it on its way out.
I also second replacing the check valve on the galley sink drain, because if this thin rubber disc fails, it will cause water to back up into the sinks & can cause flooding.