> like cast iron doesn’t have fantastic high-performance material qualities
Cast iron is a material, not a process. It's an unfortunate legacy term for very high carbon steel (>2% by weight, or <11 iron atoms per carbon atom). For reference "standard" steel is ~.08-.18% carbon, and high-carbon steel is ~.8% carbon.
The >1% carbon precipitates out into graphite within the steel, causing it to behave totally differently. Less rusting, but weaker and much more brittle when solid. Less viscous when liquid, so you can cast long and thin parts.
> Are there different, higher quality casting processes, and I’ve only seen the bargain bin results?
There are, but it mostly is independent of the material. Some turbine blades are cast as single crystals for heat stability; you can't really cut a single crystal without introducing cracks and issues. There's also vacuum casting and spin casting (using a centrifuge to force liquid into the mold), which lets you cast metals that react with air or cool too quickly for normal methods.
Most of the variation in process is about the final form you cast into, though. Engine blocks are sometimes cast into a one-off ceramic shell that is sprayed onto a sand form. It's an expensive process but it lets you do the whole thing in one step.
> is it all very complicated and material specific?
It is very material specific. Fundamentally its all about shaping the grains. In many steels you can physically alter grains. In others, like precipitation grains (aluminum alloys, some steels) the structure is determined by the cooling and you can't physically shape them. In that case you may often get a better structure by casting since you can choose how to cool parts down, while a billet will have a homogenous structure that is usually worse towards the center.