Quite correct, water is heavier than brake fluid and will eventually drain down to the caliper piston. But, because brake fluid is glycol based, it mixes with water. So, when you flush the brake lines, water is also going to get pushed out of the caliper.

I have a motivator brand pressure bleeder thing. That way I can pump it up to 10-15psi, open the bleeder and watch the old junk come out.

Removal of water is required. Water will turn to steam under pressure, and steam is compressable. The result is spongy brakes or brakes requiring too much pedal pressure to operate. Plus, water will help corrode the caliper piston.
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My back feels better when I sit in a Volvo seat