: There must be a good reason for not using the larger cutters but it is
: eluding me. Any thoughts? What am I missing?

I drew the two joints on my CAD system and found some things to consider:
First is the depth of the finished cove. When using 1/4 on 1/4 you get a pocket that is in theory 1/8" deep. If you use 3/8 on 1/4 the pocket ends up only 0.048" deep. The strips will have less "bite" with each other.
Second is the "step" that will show up when you start to go around a curve. With 1/4 on 1/4 the joint acts like a hinge and the face stays tangent to the bead. With 3/8 on 1/4 the exposed bead is not tangent to the face and creates a "step". Laying strips on a form with a 6" radius would leave a .02" step (12.5 percent of the thickness) to be removed for a fair curve.
Third, the same shift that causes a step on the outside leaves the same size hook on the inside.
Fourth, The 3/8 on 1/4 joint has 30 pecent less surface area for glue.

On the plus side, the 3/8 on 1/4" strips are about 12 percent wider.