Paul Terry wrote:

Is it me or did someone set out to make the Aldwych branch next to useless
for the main Picadilly line?

Not really ... it was more historical accident. The Piccadilly started
life as two separate lines - one from Brompton to Piccadilly and the other
from Wood Green to Aldwych. Before they were finished, these two schemes
were linked by a line between Piccadilly and Holborn, creating the first
portion of what came to be called the Piccadilly line - the consequence of
this change of plan left the short stub from Holborn to Aldwych as a
none-too-useful branch.

Perhaps - but I recall other sections of the original railways were planned
and never built. And this doesn't explain why the Aldwych branch wasn't
properly linked to the network (surely linking to the southbound tunnel as
well would have made sense?) or why the platforms were left so short, making
a through service a non starter.