The ability of coppermine to be integrated with other apps is what we call "Bridging". This is something that happens in terms of logically tying two apps together, as coppermine drops the user management and authentification it comes with in favor of the user management of the app it is being bridged with. Bridging does not take care of visually integrating stuff. But that's the main problem: if coppermine was made a genuine typo3 extension, you'd need to find a way to wrap coppermine's output into the output of a typo3-driven page. Additionally, all the GET and POST data would have to make it through the wrapping Typo3-environment into coppermine. Lastly, coppermine relies on cookies, which is something that needs to be done before any output is being generated, which again makes it hard to come up with a way to wrap coppermine into typo3.
I'm a Typo3-afficionado as well (I'm using Typo3 on several sites that I'm in charge of), so you can believe me that I have thought about this issue more than once. I couldn't find an easy way without re-writing most of coppermine's code (a complete port), which is far beyond what I'm ready to do, as it would make upgrading the coppermine component within typo3 an incredibly tedious job.
This being said: it would be comparatively easy to turn the bridging component of coppermine into a typo3 extension, but it's incredibly hard to accomplish this for the visual integration of coppermine into typo3.
I don't say that it would be impossible, but it certainly is something that won't be done by the coppermine devs. If an interessted third party wants to do that job, I'm all ears. But as far as the current coppermine dev team is concerned, I wouldn't expect this to be done any time soon.
Joachim