Illustrator and InDesign have completely different file formats because they were developed independently by different teams and for different users. Their way of handling text is also completely different. That's why they don't exchange data as well as you would like.
You could only copy small vector objects from Illustrator to InDesign, and it wouldn't retain their position so that wouldn't be practical. Formatted text can not be copied between the applications.
I would use the Place command. When you need to edit a page use the Edit Original command. You can Option/Alt-double-click on the placed AI file and it will open in Illustrator for you to make your changes. Save the changes and they will be automatically updated in InDesign.
Otherwise, you will have to recreate the entire project from scratch in InDesign.
What sorts of edits are you making?
In the long run, you're probably best off abandoning the text and recreating that in ID. As Steve says, you could copy the text unformatted as a relatively quick way to get it into ID.
While you could also copy/paste simple vectors from Illy to ID and have editable paths, I don't recommend this as it makes it more difficult to reuse the art elsewhere, and it contributes to file bloat and potential performance issues. Another possibilitly is to simply place the .ai files as may times as there are individual pieces of art on the artboard and use creative cropping to isolate them.
I'd have to open each individual page in Illustrator to make a change.
Doesn't seem like much of an obstacle if you double-click with the direct selection tool.
That's what I thought. (It's Option/Alt + double-click.) If both applications are open it's almost instantaneous.