I have it encoded in my head that $ inside "..." is respected. Subtly, the $'...' construction is not respected inside "...". After reading the manual page carefully, I realized this is because the interpretation of $'...' is not part of parameter expansion (despite its $) but rather it is a special form of quote interpretation, "Words of the form $'string' are treated specially."
However, I'm not sure that text is entirely accurate, either, as $ echo xxx$'aa\ta'yyy xxxaa ayyy "Word" is generally used to mean non-space characters (separted by spaces), but the argument of "echo" is only one word, which is not, as a whole, of the form $'...'. Dale