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How to straighten image along a path

I have a challenge that I think should be easy but is probably not:

I want to take the writing around a coin and straighten it out. Perhaps I'm thinking of a tool in Illustrator (which I've never used) where I can "draw" a curved path then force the path into a straight line.

I've been messing around with warping but the results are too crude.

Any ideas appreciated.

Anyone, can this be done?

As a test I've tried warping a simple curved line into a straight line and find it impossible. Would love any ideas whatsoever!

Yes, but it doesn't need to be. That's just my particular project. A better example would be taking to take a rainbow and straighten it into perfectly straight colored bars.
Ras, The point isnt to straighten the existing words. Use the clone stamp tool to remove them. THen once they are removed use the font tool to place new font. Its as easy as that.