The <think> blocks are an attempt to explore the gradient descent space to escape local minimums and find a better global minimum to continue the descent.
While verbosity _might_ do this better, you could easily consider things like "but wait am I forgetting ...." as just one token. So if you actually do it right, you could replace all that with a "hold on" or something of a terse variety.
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.