Is there any kind of paint that would actually paint on rough on purpose?
You can buy pretextured paint. Behr makes it and can be found at Home Depot. Here is an article regarding pretextured paint.http://www.painting-ideas-techniques.com/texturedpaint.html
Yep! Textured paint.
We used to call it sand paint. You might use it on a porch or stairs. The walls in one of our homes had a sand paint texture. Over the years various layers of paint changed the texture and it was impossible to recreate.
Grip paint is made to make surfaces more safe. They usually carry them at the big box stores like Lowes or Home Depot.
Try and do a test patch adding beach sand to your paint.
Look into Saltwash paint. It gives a nice, rough, worn texture.