I'm saying quite the opposite, I'm saying that the longer texts are produced not only because they hold more information, but because they are necessary in producing the correct information.

A simple example, if you have two models Short and Long, and ask "what is 1942848x41482982", the Long model might answer in 300 tokens by expanding the operation and producing intermediate factorizations and solutions. While the short answer will simply produce the output. However since the Long model actually developed its answer instead of hallucinating it, it will more often be correct.

It's not that more text holds more information, but that more compute can solve more problems correctly. Limiting output length in models is effectively reducing compute, which obviously will lead to less correct answers.