Is it really necessary to physically cross (interlace) the spokes on traditional wheel lacing?
Probably the best source for answering this is Jobst Brandt's The Bicycle Wheel, the definitive text on the wire-spoked wheel and an essential for anyone interested in the art of wheelbuilding.  Excerpted from page 68 of the 3rd edition:


  Spokes in a crossed pattern are usually interlaced at their last crossing before reaching the rim. Spokes coming from between the flanges are laid over those from outside the flanges. Interlaced spokes take up each other's slack during severe radial loading and reduce the chance of spokes becoming loose. If spokes become loose, their nipples can unscrew. Radial spokes cannot be interlaced and therefore, lose alignment from road shock more easily. Interlacing also gives more clearance between the spokes and the derailleur on rear wheels.