The original External Tank nose cone design was indeed blunt - almost like a fireplug, as seen in this 1975 concept art.

[Image source - lost in the mists of time to me, but NASA somewhere]
However, wind tunnel testing at the Arnold Engineering Development Center revealed that this configuration caused unsteady aerodynamic buffeting at some conditions. A bi-conic spike design was conceived and further wind tunnel testing showed that it eliminated the problem.
The nose cone served several functions besides its aerodynamic one.

[Cropped from https://www.nasa.gov/centers/marshallimages/content/149235main_IMG_2558_3072x2048.jpg ]
- It also covered the LO2 vent/relief valve and provided vent exits for
gases boiled off from the LO2 tank, which were subsequently carried
off by the "beanie cap" umbilical arm.

[Image Source https://contactsam.files.wordpress.com/2014/11/vent_arm_141113_2.jpg ]