Sorry. I'm thinking ahead of my post. The issue is that the water that sits in the hot water lines gets cold while its sitting there unused. In order to get hot water, you have to pump water through the hot water lines continuously, and this is best done with a tank of hot water that you can just recirculate. When you have a tankless system, that means, at best, turning the burner on every few minutes to get new hot water to keep the lines warm, and since there's no tank to recirculate that water to, it just gets wasted. And that means that it's no better than what's going on now, but you don't get any water savings. At worst, you need a pump to deal with pushing the water through a closed system that can no longer be gravity fed, and installing a pump on a tankless system won't really work, so you can't fix it at all.

Of course, IANA plumber, so I could be wrong, but that's how I understand it.