Why would a gearset be designed like this? (two-piece/grooved gear) 1

It may be an anti-backlash system.

It is indeed an anti-backlash system to reduce noise. The narrow part of the gear will be spring-loaded in the reverse-torque direction.

Toyota 2RZ-FE or 3RZ-FE by any chance?

It's called a scissor gear. They're used on engines with cam/accessory gear drives to reduce dynamic tooth loads due to torsional oscillations. In the case of your Toyota cam gear, the torsional oscillations are produced by the varying forces acting on the cam lobes. There is a moment in one direction as each leading cam flank pushes a valve open, and a moment in the opposite direction as the valve spring pushes against the trailing cam flank during closing. Conventional gears (not scissor gears) require some amount of backlash at the mesh to prevent interference. When there is backlash, reversing torsional oscillations will cause high dynamic contact loads on the gear tooth flanks at the mesh. These high dynamic tooth contact forces also produce noise. While a scissor gear can reduce dynamic tooth loading and noise, it also involves some mechanical losses.

You'll see them used on other engines like Cummins diesels and Honda motorcycle engines

Here's a video that shows the Toyota scissor gear internal parts.

Very interesting - thanks guys for the clarification! I had never heard of scissor gears however it had not occurred to me that there might be a spring in this assembly. I had considered it might be involved somehow with mitigating backlash however I was not thinking of there being a spring, and I would have thought a fixed assembly that eliminated backlash (ie: two gears pinned/clocked where one contacts the forward and one contacts the reverse flank) would run into the same issues that a traditional gearset manufactured with zero backlash/interference would. A spring setup would definitely make more sense, albeit with the drawback you mentioned of some mechanical losses - I assume directly related to the stiffness of the spring used.