It might as well have built itself, for all the involvement Shepard had.
Why does Shepard need to be directly involved? I might want my engineer looking under the hood, but I vastly prefer that the galaxy's best and brightest minds handle its construction, while Shepard bolsters the diplomacy, resource/personnel allocation, and Reaper fightin' while it's being built. If you don't see that as involvement, then again that's entirely on you.
And ultimately it was Bioware's handwave that decided what it did.
Yes, they wrote the capabilities of the Crucible, and two of the three adhere perfectly fine to tech principles in the narrative (with the third one being entirely optional).