As Lordofduct noted, the Saturn does have hardware transparency capabilities, but it's not as simple as they only work in 2D and not in 3D. Apparently Sega had a minor problem and implemented them on the Saturn incorrectly. They work in most cases but there's a bug in how they operate that keeps them from being used easily in some scenarios. That bug is what makes them totally unworkable in 3D. The Saturn games that feature transparency in 3D space are usually just programmed with software transparency calculation.
The SNES also had limited transparency capability. It could only be used in certain ways. That's why in some games everything in the background will be transparent but sprites will often disappear or remain the same color even when behind a transparency. The SNES's implementation is even more limited than the Saturn's naturally.
Sorry I'm so light on details. This is from a conversation I had with a US Saturn developer a few years ago, so I'm pulling from memory, here.