Longer poles certainly look more majestic, but our experience has shown that by reducing pole length we also reduced rain running down the poles. Having long poles probably had more to do with status than any practical use, the Indians used to drag the poles when on the move and this would constantly wear away the tips of the poles, for plains Indians, lodge poles were an expensive outlay. On the plains the rain usually came in sideways blown by the wind, turning the smoke flaps or closing them would keep out most of the rain, what rain did come in fell into the fire pit or ran down the poles, here in France and many parts of Europe the rain comes down like stair rods straight into the centre hole, that is why having shorter poles with a rain cap is essential, our poles only stick out by about 2ft-3ft. Cutting poles to exactly the same length ensures you get a natural slope for rain to run off.
You raise some valid and logical points. And to be honest I don't know just how big a tipi the OP wants to make. But size indeed likely had something to do with the traditional native ones. By that i mean size (circumference/diameter at the base) in ratio to height. While a shorter one would provide the advantages you describe, we have to remember that for the Native Americans, they weren't "camping." It was their home. They actually lived in it with their families. Their tipis had a diameter at the base much larger than any modern camping tipi (likely around 20-30 feet in diameter) Can you imagine how little headroom they'd have (except in the center) if the tipis had been shorter?
Granted, these likely aren't concerns the OP need worry about.