As i understand it, the clearances between the stator and turbine stages are wider than those of a typical turbojet engine to allow them to operate as a "ram-jet" above a certain speed threshold, making them difficult to start. why they didn't use a gear type pneumatic starter is beyond me, but perhaps it had to do with weight savings, or the extreme operating conditions. Everything about them was so secret and compartmentalized, and a lot of the original engineers are long gone. With today's materials and tech, the same folks might have done it all very differently.
Add to that the sound of a throttling big displacement V-8 under a load, a serious morale booster for some fellas, certainly more musical than the ear destroying rush of a turbine.
Here's a cheesy animation of the J58:
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