I just got off the phone with the attorney who drafted our bylaws.  He told me that the format we have for elections of officers in the norm in Ohio.  Under Ohio law it takes a 75% vote of the membership to remove a director.  If we went to direct election of officers, this same threshold might apply.
The most important reason to have the Board elect the officers is to allow careful monitoring of the officers.  The membership at large can not keep track of the actions of the officers in the same manner as the board.  If an officer of the corporation was elected, then found to be stealing from the group, the delay required to replace them by a vote of the general membership would be  disastrous.
We are set up in the same manner as every corporation in the U.S.  There are reasons that all corporations are formatted this way.  To try to redo the basic corporate structure, with the careful checks & balances that are firmly in place with some new hybrid sounds risky and silly.
Please keep in mind that under the bylaws, the board is in charge of the organization.  The president has duties, but no real power beyond what the board allows.  If there is a clash on who should be president, the general membership needs to elect board members that reflect their ideas.