Prevent WordPress from sending set-cookie http header

I could see this being a really common issue for page speed where you don’t want to lose the plugin, but you do want your homepage to rank well and come nice and fast from cache and it doesn’t need various cookie wielding plugins breaking cache on the homepage.

If that was the case… could you just do a Snippet like…

if( is_homepage() ) { 
    header_remove('Set-Cookie');
}

(pseudo code / untested)