When you want to show/hide comments on page/post of your site click on "More tools and options":
then tick "Discussion":
and enable/disable the option "Allow Comments" as shown in the screenshot below:
You can also globally disable comments for pages, by default:
Adding such an option would technically change core WordPress functionality and themes are not allowed to do this. However, there are several plugins which can do this without messing up with the way comments work in WordPress. Here are some examples: