Paul Terry wrote:

That explains why it was built but not why the connection at Holborn is so
useless.

I suspect that by the time it was built, it was already obvious that
Aldwych would never be more than a rather useless stub.

In which case, a great lack of foresight. Had an extension later become
available then a Waterloo to King's Cross St. Pancras direct route could
have been constructed. (Isn't something similar floating about in current
official long term pipe dreams?) Even just as a reversing bay the line would
have been of some use - what are the current cut-off points for truncated
services on the Picadilly?