A workflow similar to ReSharper's Code Cleanup was introduced in IntelliJ IDEA 14 in late 2014.
Since WebStorm is based on IntelliJ IDEA platform, I assume that it's going to incorporate Code Cleanup soon as well. The current production version of WebStorm, v9, was released in October (that is, before IJ 14), making WebStorm 10 a good candidate to include Code Cleanup. Now, WebStorm 10 Early Access Program (EAP) doesn't list this change so far: either because it's not there so far or because the WS team just didn't include the feature in a summary of changes.
I'd say grab WebStorm 10 EAP and check if there's a Code Cleanup item under the Analyze menu, and if it's there, check that it's doing what you expect it to do.