A
That's not actually correct. Watch the control monitor of Toaster system when doing a transition. The animated effects are done by the Amiga, you just can't see them well because they are encoded with extra data that doesn't look correct on that monitor, somewhat similar to a DCTV image. It's a combination of overlay, matting and UV coordinate information that the Toaster card knows how to interpret. The gate arrays on the Toaster card then use that data to mix the video signals and potentially the decoded Amiga graphics.
Okay, but that's very sparse data. It's not heavy lifting at all. It's very clever, allowing new effects to be added without the need of firmware updates to the board. I would put money on this actually being less work than a full page of Kara Fonts characters scrolled from the bottom of the screen to the top. Some polygons and a few "magic bits" is hardly "Only Amiga Makes It Possible" material.
The Amiga Toaster had chips that processed video, but the mix was driven by the Amiga. The video didn't need to get to the host computer unless you grabbed a still, which is a very slow process on a Toaster.
You're using "mix" here as if it was actual work or some kind of special engineering. The video was processed on the board and sparse data sent from the Amiga instructed the board. It's not magic. If I'm watching Netflix streaming over a Chromecast device yet I'm controlling the Chromecast with an app on my phone I don't attribute any of the streaming or display or decompression, etc. to that mobile device in my hand.
That's a very simple analogy, simpler in many ways compared to what is happening in the Amiga to Toaster connection but there is nothing stopping an extension of this very sort of one-way relationship of control such that full scrubbing and editing and higher level application control is established in such a paradigm and no matter what I would never attribute any of the real work to the handheld device that's ultimately controlling and "driving the mix".
Going with smarter, more specialized hardware would also limit the lifespan and flexibility of the design. Those cards only became outdated when HD video became the norm.
Mmmmm, in local TV circles and the like, perhaps, which stay with hardware long passed its sell-by date. The Toaster became anachronistic with just a notch above the the more common industrial level (limping along on U-Matic) not long after the release of the VT4000. Because composite video. It would be the late 1990s but well before HD when the VT and its composite video became a real problem at the prosumer level. Because IEEE 1394, otherwise known as Firewire.
As soon as video acquisition and recording went digital the Toaster was pretty much public access television material. But by 1993 even, component video devices were making their way into prosumer hands even, via devices like the Personal Animation Recorder and later Perception Video Recorder. These rendered the framebuffer and video output on the Toaster a null and void issue for pretty much any application not involving the switching or processing of live video.