I'd like a club president ..... elected by the members
Even the prime minister isn't directly elected by the voting public.....
And that somehow makes it okay?
No. Just saying it's unusual and not practical.
Hopefully, if you can actually elect all members of the board, you can trust them to vote in the best person to lead them.
No issue with that Y&BB 
A PM still needs to face the voters within his own electorate every three years to keep his seat in parliament. As Stanley Bruce and John Howard found out in the end, that's not always a certainty. Once you win the approval of the local voters to represent them, then your party caucus can vote you as their leader and, if in government, PM as well.
The ability to appoint directors was argued by its proponents as being a means to attract people with certain skills onto the Board who would be reluctant to do so if they had to face a election to gain position on the Board. It was never mentioned as being a means to enable existing directors, and in this case the club president, to bypass the scrutiny of a members' vote.
