set -e (no || or &&)

[Sergey Fadeev]

Why doesn't it exit the shell?
 $ set -e
 $ echo $(false)
 Shouldn't the error code of $(false) command substitution be checked by set -e 
before passing stdout to the echo builtin?
 Isn't it the most logical behavior that most people would expect of set -e?
 Bash version: GNU bash, version 4.2.24(1)-release (x86_64-redhat-linux-gnu) 
(if it matters)
 Thanks