FPGA is really expensive for the scale of a modern studio render farm, we're talking around 40~100k cores per datacenter. Because 40~100k cores isn't Google scale either it also doesn't seem to make sense to invest in custom silicon.
There's a huge I/O bottleneck as well as you're reading huge textures (I've seen textures as big as 1 TB) and writing constantly to disk the result of the renderer.
Other than that, most of the tooling that modern studios use is off the shelf, for example, Autodesk Maya for Modelling or Sidefx Houdini for Simulations. If you had a custom architecture then you would have to ensure that every piece of software you use is optimized / works with that.
There are studios using GPUs for some workflows but most of it is CPUs.