I can see the point about the hot running hot and cold running cold, actually. And Howard's point about the cold water being fresh and not stored...does make a lot of sense. It is really nice that our cold water comes out almost like a running brook in early spring...nice and crisp, if that makes any sense.
We get around both these issues (somewhat) with a combi boiler. (I love the combi boiler idea.) Yes, there is a bit of "old" in the pipes when you first run it, but I think all taps have this going on. The "mixing" bit for us is right at the end, just before the water comes out. The tap is like an upside-down "Y" shape. Well, not really, but it works for me as an explanation.
![Wink ;)](https://www.talk.uk-yankee.com/Smileys/classic/wink.gif)
I'd hate the square taphead, too. Ours isn't square, though, and probably would fit a hose...except that we have a tap on the outside wall that we use, and that only runs cold water.
We've yet to install a master bath and I'm giving some thought as to the pros/cons of mixer v non-mixer taps. I'd like it to be traditional so perhaps non mixer is the way to go. Hmmm...