Art Unwin wrote:
"When one looks at a radiating array pattern one can see that the yagi
is very inefficient."

Efficiency is output over input. Antennas can be made very efficient.
When radiation resistance is large in comparison with waste (ohmic loss
resistance), efficiency is high. Directivity is something else.

Often, Terman answers antenna questions simply. This is such an
occasion. Terman writes on page 907 of his 1955 edition of "Electronic
and Radio Engineering":
"The Yagi antenna of Fig. 23-39, and the corner reflector, represent
about the best that can be achieved with respect to edirective gain in a
compact array."

Pity the fool who argues with Terman or Kraus.

Best regards, Richard Harrison, KB5WZI