According to former Apple executive Tony Fadell -- these days remaking the thermostat -- Apple's designers had extensive discussions about including a hardware keyboard on the iPhone, but ultimately decided against it. Fadell discussed the iPhone design process in a sit-down interview on Josh Topolsky's On The Verge show.
I wanted to try [a touchscreen keyboard]... I wanted it to work. It made sense that you wanted a full screen, you didn't want a keyboard.
Fadell also mentions the other designs for the iPhone, including the iPod + Phone concept using the iPod click wheel as a controller, but noted that the team ultimately discarded that concept because the control scheme was too restricting.
Apple's designers make many prototypes that never hit the light of day. We didn't know it at the time, but the iPod with click-wheel dial that Steve Jobs jokingly showed at the original iPhone announcement wasn't too far off from something Apple had actually created.
In his biography, we learned that Jobs had set up two competing teams to find the best iPhone design. One based its designs off the existing iPod, while the other designed a brand new touchscreen system that ultimately became the iPhone.