HSTS: You still need to set the Secure flag on cookies*

If you have HSTS enable do you still need to set the 'secure' flag on cookies or is it redundant?
Its possible for an attacker to modify Cookies from sub-domains, so not setting the "includeSubDomains" when configuring the Strict-Transport-Security header would allow a range of cookie-related attacks that HSTS would otherwise prevent by enforcing a valid certificate for a subdomain.
So setting the "Secure Flag" is set on all cookies will also prevent, some, but not all, of these attacks.