Can't you simply not use the spacers, tighten the nut to the appropriate bearing play, put a cotter pin in it, and call it a day like other cars?
Hi, Casey - welcome to the forum!
Nope, you can't do that - referring to the cross-section of the rear spindle below:
The key characteristic of low-friction tapered roller bearings is that they will carry huge radial loads, but they can't be axially preloaded at all, or they'll fail. Front wheel bearings aren't preloaded, which is why the adjustment procedure is to tighten the nut up to 12 ft-lbs. while spinning the hub to seat the bearings, then back the nut off one flat and insert the cotter pin (that will set axial clearance at .008" or less).
The tapered roller bearings on the Corvette rear spindle are no different - they can't be axially preloaded either or they'll fail.
The outer bearing inner race is a press-fit on the spindle, and the outer race is a slip-fit in the spindle support; the inner bearing races are a slip-fit on both the spindle and in the support. The tubular bearing spacer and select-fit shim (fitted to ensure that there is at least .001" axial clearance between the two bearings, and called the "bearing preload spacer" in the cross-section below) are required in order to maintain the clearance after installing the drive flange, which bears against the inner race of the inner bearing, and whose attaching nut is torqued to 100 ft-lbs to retain the flange on the spindle.
The spacer and shim create a solid stack from the inner race of the outer bearing to the inner race of the inner bearing and the drive flange, while maintaining the necessary axial clearance in the bearings.
If you left out the tubular spacer and shim and torqued the drive flange nut, that would pull both the inner and outer bearing rollers against their race tapers into interference, and the bearings would fail almost immediately. Tapered roller bearings CANNOT be preloaded in any way or they'll fail, and if they have excessive clearance they'll fail; the design must provide for the required axial play, and must not allow the clearance to be reduced or increased during operation in order for the bearings to operate reliably, and that's what the spacer and shim do.