Shaft drives aren't *that* inefficient. With the best turn of the 20th century machining, they were about 92% efficient. Engineers could do better today.

Major Taylor broke more than one record riding a shaft drive.

Chains, when maintained adequately, are almost 99% efficient, however.

The most important disadvantages of a shaft drive are its much greater weight, and its greater cost. It's much more expensive to machine to the tolerances required by a shaft than a chain.