Most licences require derivative works to be under the same or similar licence
Some, but probably not most. This is mostly an issue with "viral" licenses like GPL, which restrict the license of derivative works. Permissive licenses like the MIT license are very common and don't restrict this.
MIT does say that "all copies or substantial portions of the Software" need to come with the license attached, but code generated by an AI is arguably not a "substantial portion" of the software.