First and foremost, if you're using only an image as your email signature, you're at risk of your emails being treated as spam. This is because the text:image ratio is too low.
Secondly, using only an image as your email signature, doesn't allow you to make different parts of the email signature clickable. It might not take your customers or business associates to what they might be expecting when they click on something in your signature.
Lastly, an image-only signature is invisible if the recipient has image blocking enabled on their end. Instead of seeing your text content, they’ll see an empty box with either the dreaded red x or a message saying images are disabled. That could easily mean clients and potential clients will not see the brand you’ve worked so hard on.