I am sure that you can "manage" to get down to the bottom some how but it won't be easy or convenient .... Why spend your energy and your precious air kicking like mad to get the desired depth (if you stop kicking, you'd lose ground and float up to the surface)??
In the SCUBA classes I took, we had to be able to pike dive to the bottom of the pool to retrieve our weight belts after rescues. This was usually in full exposure gear. It took a total of zero fin kicks to make it to the bottom of a 14' pool. If you intend to be neutral at 15' at the end of the dive, you're going to be heavier by the weight of the gas you're going to use, and most definitely negative by 15'. Under these conditions, you will never need to kick down at all.
What about if you are involved in some sort of an U/W activity such as spearfishing, photography, U/W survey, etc.? How many tasks are you going to be able to handle? What about an instructor who is handling a class with students going up and down? The list goes on and on.
I think skipping the wing decreases task loading, not increases it. Most of the adjustment comes naturally and unconsciously. I would wear a wing if I was assisting with a class (even if not required by standards) in case I needed to establish extreme positive buoyancy without ditching weight.
If you are worried about losing a skill, so what? I am gaining another skill that makes it much more convenient, safer, more comfortable, more enjoyable while losing nothing.
I say this without intending to cause offense. In my personal experience, learning that I could dive without a wing has given me better understanding of diving and buoyancy control, and it has given me the opportunity to really be able to tune my weighting for a particular situation.
I believe that a method to establish positive buoyancy on the surface is essential, and that most people are reluctant to drop weights. For this reason, I believe that the BC is a helpful addition for most divers. When I dive without my wing, I wear my weights on the outside of my harness, wear a snorkel and carry a 40lb lift bag. For most of my diving, I use a wing.