And here another little detail: I installed Babun on the Windows 10 machine.

juergen@saraswati ~
$ value="$( date | cat )"; echo $? $value
0 Tue, Jul 11, 2017 10:24:02 PM

juergen@saraswati ~
$ echo $BASH_VERSION
4.3.33(1)-release

juergen@saraswati ~
$

It works.

The BASH_VERSION on the other Cygwin installation is 4.4.12(3)-release.
The command substitution with a pipe doesn't work there.