As a parallel case, consider multi-ply composite construction, where sheets of fabric, sometimes of sheets with a single fiber orientation, are laid at angles to each other to spread the loads in exactly this way. They both better approximate an isotropic material, and are stronger than an equivalent thickness of singly-oriented plies all in the same orientation.
Gears are subject to predictable stresses, and so being able to orient a material to best handle those stresses will make a stronger gear. Plywood, like anything else, is a compromise that, as you say, has a more isotropic character. Obviously, there is a wide range of strength in wood, and so plywood. I think it's reasonable to say that one could construct a stronger gear using teeth from readily available solid wood, then readily available plywood. Good luck finding hickory plywood :).
To your first sentence though, if you take the same size and quality solid board and piece of plywood at your local hardware store (making a reasonable attempt at an apples-to-apples comparison), the board will be almost certainly be stiffer and stronger with the grain, than the plywood will: https://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr190/chapter_...
He uses the gears in many heavier-than-you-would-think-duty applications.
Mathias was an engineer for BlackBerry Ltd. before he retired young.