Symetric key encryption is not Authentication? Is there any way to show CCA-secure symmetric-key encryption does not have to be an authenticated encryption?

I know you can create a setup that isn't authentication, but how will you go about it?
Consider a CCA2 secure secret key encryption scheme $\mathcal{E}$ with an exponentially large randomness space. Turn this into an encryption scheme $\mathcal{E'}$ where we extend the randomness space of $\mathcal{E}$ with one more element. Let's think of it as $0$ (we can get there by rearranging the randomness space). For randomness $0$ the encryption in $\mathcal{E'}$ becomes the identity for every element.

Now, I claim $\mathcal{E'}$ is still CCA secure as the probability that for the challenge query randomness 0 is chosen is negligible. However, $\mathcal{E'}$ is not a secure MAC as everybody knows a valid tag for any message.