There are a number of reasons to choose a vertical clutch design.
First I am not going to dissect the original Seiko design. I am working on that task separately.
However, there are several performance reasons to go with the vertical clutch design.
1. The ability to run the chronograph continuously. With "traditional" supplemental fourth wheel/intermediate wheel/center wheel chronograph train designs, the teeth on the center wheel are triangular in shape and very small and fragile. The teeth must be small and of this shape to minimize jumping when the chrono is activitated. However, this leads to substantial wear issues. I can't think of a single chrono of this design where the owner is not specifically advised NOT to run the chrono continuously because of wear. Vertical clutch designs permit constant running of the chrono if the owner desires.
2. Rate keeping. The gear design produces on average around a 30 degree drop in amplitude when the chrono is activated. Thus rate keeping suffers. This does not happen with vertical clutches to anywhere near this degree and again the chrono can be left running with little effect on rate keeping.
3. Start stopping. With gear designs it is a crap shoot how the teeth will land when the chrono is started. Sometimes fate smiles and the peak of one tooth happily lands in the trough of its mate. More often that is not true and the chrono hand will jump as a result. This is simply unavoidable. With vertical clutches, starting is essentially always smooth.
4. Avoidance of needle flutter. Gear designs suffer from fickelness. Chrono second hand movement has a tendency to produce flutter, which is uneven movement. There are two techniques employed to minimize this. Most commonly a spring is tensioned across the chrono seconds hand shaft to apply resistance to it. This has the disadvantage in that reduces amplitude, effects rate and consumes energy. Alternatively the depthing of gear engagement between the center chrono wheel and intermediate wheel is increased. This puts tension into the train and at worst can stop the watch. I cannot tell you how many absolutely top of the line chronos I have seen that suffer from this flutter problem. This does not happen with vertical clutch designs.
So there is much more going on than cost.
Jeff