You're probably right that, in practice, the character class doesn't automatically add security if the password is sufficiently strong and random. The theory is that by introducing special characters you're decreasing the likelihood of having characters that are commonly found together, thus decreasing the effectiveness of dictionary attacks.
Of course modern dictionary algorithms will still look for characters that are commonly used as substitutes for letters ($ = s, # = h, ! = 1 etc.) so really you just want your password to be random, long and unique.
The NIST guidelines address that in a much more straightforward way: maintain a list of known bad passwords (e.g., HIBP) and prohibit users from using any of those. Character class requirements are pointless.
