How to escape history expansion exclamation mark ! inside a double quoted string?

If History Expansion is enabled, you can only echo the ! character if it is put in single quotes, escaped or if followed by a whitespace character, carriage return, or =.

From man bash:

   Only backslash (\) and single quotes can  quote  the  history
   expansion character.

   Several  characters inhibit history expansion if found immediately fol-
   lowing the history expansion character, even if it is unquoted:  space,
   tab,  newline,  carriage return, and =.

I believe the key word here is “Only”. The examples provided in the question only consider the outer most quotes being double quotes.

In your last example,

echo "$(echo '!b')"

the exclamation point is not single-quoted. Because history expansion occurs so early in the parsing process, the single quotes are just part of the double-quoted string; the parser hasn't recognized the command substitution yet to establish a new context where the single quotes would be quoting operators.

To fix, you'll have to temporarily turn off history expansion:

set +H
echo "$(echo '!b')"
set -H

Sometimes you need to make a small addition to a big command pipe

The OP's "Good, but verbose" example is actually pretty awesome for many cases.

Please forgive the contrived example. The whole reason I need such a solution is that I have a lot of distracting, nested code. But, it boils down to: I must do a !d in sed within a double quoted bash command expansion.

This works

$ ifconfig | sed '/inet/!d'
inet 127.0.0.1 netmask 0xff000000
…

This does not

$ echo "$(ifconfig | sed '/inet/!d')"
-bash: !d': event not found

This is a simplest compromise

$ echo "$(ifconfig | sed '/inet/'\!'d')"
inet 127.0.0.1 netmask 0xff000000
…

Using the compromise allows me to insert a few characters into the existing code and produce a Pull Request that anyone can understand… even though resulting code is more difficult to understand. If I did a complete refactor, the code reviewers would have a much more challenging time verifying it. And of course this bash has no unit tests.

This was repeatedly reported as a bug, most recently against bash 4.3 in 2014, for behavior going back to bash 3.

There was some discussion whether this constituted a bug or expected but perhaps undesirable behavior; it seems the consensus has been that, however you want to characterize the behavior, it shouldn't be allowed to continue.

It's fixed in bash 4.4, echo "$(echo '!b')" doesn't expand, echo "'!b'" does, which I regard as proper behavior because the single quotes are shell syntax markers in the first example and not in the second.