Let's just agree to disagree on this one. A couple of points to make:
1) The preferred natural state is equilibrium. The brake fluid will mix, otherwise you wouldn't add new brake fluid to old brake fluid as you'd have a system with multiple states.
2) Pull out your fluid mechanics manuals and you'll see that since their is an up and down piston action against a barrier/closed end, it should follow normal internal flow properties. The fluid velocity at the barrier is obviously zero and the fluid velocity in the circumference of the line is <0 at some point through the circumference the line. So, the fluid is going to move with each depression and release in opposite direction to the piston.
3) I believe the laws of diffusion apply here as well.
All of that said, yeah bleeding the lines makes sense, I don't disagree, especially if you've heated things up a bit.
One other thought too, if there was no circulation and the only point of entry is the reservoir, then how does water make its way to your calipers?
It's been some time since I took fluids, but there is no need to brush up on my Navier-Stokes. Your application of the principle you mention is highly idealized. You are talking about a very small amount of fluid displacement every time you hit the brakes. Also, the conduit has a, what, 1/8" diameter? and a length of many dozen to a couple of hundred inches in length. You think your piston moving a tiny fraction of an inch is going to circulate fluid much?
Anyhow. I get your approach. I've done it on a coolant system on a previous car where getting the last 10% out was a PITA, so I drained 90% and filled it with good coolant, and a few weeks later did the same. Still not ideal, but mostly there. The difference being that there is a water pump circulating the coolant. That doesn't happen on brake lines.
Also, brake fluid doesn't mix so easily. There is a reason people successfully put new fluid and let it push the old fluid out.
Finally, water doesn't make it into you lines all that easily - air does. Water is incompressible and would not affect the feel of your brakes. It is air, with much smaller molecule size (why Gore Tex works) that can find its way in, and it being compressible will make the pedal feel spongy, thus requiring a brake fluid flush.
Maybe this all explains why I have never heard of anyone just replacing brake fluid at the reservoir and hoping it will all mix nicely as a way to avoid a proper bleed/flush.
But yeah, let's agree to disagree.