Q400 First Officer reports being dispatched from a high altitude airport with an MEL requiring manual pressurization. Reporter believes that the constant attention required of the non-flying pilot is detrimental to the safe operation of the flight.

Narrative

We closed the forward PAX door and went to finish below the line on the Before Start checklist. The left aft passenger door showed open. After talking with maintenance the door proximity sensor was MEL'd and we proceeded to LAX. I believe flying manual pressurization is compromising safety; especially when departing ZZZ and landing in LAX. If an engine quit in ZZZ; we'd have to fly that horrendous complex special procedure; which is hard enough when everything is working. Also trying to manually pressurize the airplane while running checklists; flying the airplane; and talking to ATC is aggravating the situation. LAX is very very busy airspace; with multiple level offs; that require constant attention to the pressurization system (monitoring pilot head up monitoring the pressurization; but nothing else); is something that should not be required during the sterile flight. We aren't allowed to have non-essential talking below 10;000 feet; but we allow one pilot to be completely out of the loop to deal with the proper pressurization of an airplane at this time. Manual pressurization is a safety risk and should not be done with passengers on board period!