You cannot do this out of the box. You will have to create a customised solution to do this, by implementing a custom controls for instance.
When you start using Sharepoint you need to change your mindset about whatever you used before. Believe me you don't want to pick a fight with Sharepoint, because the beast will win.
back to your problem I think you should be looking at Reusable Content.
Here is a description about it:
http://en.share-gate.com/blog/sharepoint-reusable-content-a-forgotten-beauty
Basically you have a list where you manage all your reusable content bits (sort of like your files).
And then in the Rich text editor for the page content you can then insert a snippet that inject your reusable content.
if the content changes all the places you are using the reusable content bits will also change.
So this behaviour is pretty much the same you get if using a file. Except it's the SharePoint Way.
Good luck