8888
To eradicate that specific whine, you must understand what is happening first. Obviously turbines are meant to run at high revolutions - not at starter revs. At light off, you have a mass expulsion of exhaust gas being fed over an 'effectively stationary' high speed turbine. As the turbine is not aerodynamically suited to this slow state, it cavitates/stalls (not the typical compressor stall you know) in sections (that's the whine) until it accelerates and stabilises within its operating envelope.
If you can drive the high speed rotor faster before light-off, no whine is produced. A big engine with only 2 spools needs a massive amount of bleed air demand (high pressure) and hence more robust bleed plumbing and starter. In the interest of commonality and dollars... Question is, do you want to?