When you say "cast", think if cast iron or cast plaster. This use of the word is to shape something when soft and then to let is harden. This is what we do when we write in in. we cast words or spells in ink.

Then consider the word "broadcast". I am not using ink but, as I type this message it is changeable like soft iron or soft plaster. Once I "broadcast" this message it will be cast abroad , unchangeable as is cast iron or a plaster cast. You could say that I am "casting a spell broadly" or that I am "broadcasting words". Means no different.