Interior space. Any roundish shape with more sides more closely approximates a circle, which has the most area for its perimeter. This makes it more efficient in terms of usable real estate. The absence of a central pole has obvious advantages, especially when that's the common location of a heating and cooking fire.
Exterior space. Guy ropes would quickly make a problem for a cluster of shelters. They'd become a trip hazard and would require more space between tepees.
Stability. Tepees are fairly tall, so the unsupported panel between poles would have a lot of free play. In breezy conditions there would be a lot of flapping, which is noisy and inconvenient. More poles means narrower, more rigid panels. In some regions setting robust stakes in the ground for guy ropes is very difficult.
Strength. Poles tend to be long and narrow (often lodgepole pine), and the hides used to cover them are not like modern fabrics (at least traditionally). They're heavy natural animal skins. That, plus moisture from rain and show, can weigh hundreds of lbs. You wouldn't want to risk having that come down on you as you sleep.
Availability. Modern rope wasn't available historically. Trees were. Leather strapping and other natural rope was difficult to produce in quantities necessary for a stable, durable structure.