Why are wings not tapered all the way to reduce vortex drag?
One of the approaches to reducing this drag is taper the wing

No, not at all. The vortex strength depends on the lift at the center wing. This strength invariably tapers to zero towards the wingtip, regardless of the wing's geometric taper ratio. The taper ratio will only change the local gradient, not the absolute decline in vortex strength. In the end, what happens at the tip is insignificant for the shape and strength of the wake.