The Video Toaster used the Amiga's ability to sync to a video clock supplied by a card in the special video slot. But the Amiga itself didn't include a video input for an external source, so the Toaster hardware card included that external input. However, other Amiga video add-on cards did the same. The real magic of the Toaster was how it heavily relied on the Amiga's blitter and other custom chip-based graphics abilities. So much so the Amiga's partial genlock ability wasn't even essential to the Toaster existing. In the 1980s one of the most difficult and costly parts of a real-time digital video effects system able to remap live video inputs interactively was the address generator which told the hardware where to remap the pixels 59.94 times a second. These addresses have to be generated at video speeds which wouldn't have been possible at full broadcast video resolutions by any other mainstream computer of the time. For example the Mindset computer was released the year before the Amiga and had a full genlock built-in but the Toaster could never have worked on it because the Mindset wouldn't have been able to generate the addresses fast enough.

If another non-genlockable computer could have generated the remapping addresses fast enough in those days, a Toaster-like device could have been designed to work with it. It just would have had to include a full separate genlock and the output would have been delayed a frame to allow that circuit time to work. So, it was possible, it just would have cost a bit more. How much more? Around that time, separate genlock cards capable of syncing up two disparate video sources sold for around $1,000.

On the other hand, an interactive, real-time address generator capable of keeping up with full video speeds would have cost tens of thousands of dollars. For example, the Quantel Mirage cost $700,000 in the 1980s and didn't even generate its addresses in real-time. The Mirage pre-rendered all the remapping addresses to a massive RAM disk using a Pascal program running on a workstation (which could take an hour or more) and only played them back on cue. The real-time part of the Mirage's hardware just digitized live video input and mapped it to the fixed stream of pre-generated addresses. Thus the Mirage could apply complex effects to live video but the effect geometry had to be canned, not interactive. The Ampex Digital Optics hardware did generate addresses in real-time entirely in logic-gate based hardware. Take a look at the ADO patent to gain an appreciation for just how insanely hard it was for 1980s era pre-GPU hardware to generate addresses at broadcast video rates. (https://patents.google.com/patent/US4472732/en) In fact, these esoteric real-time broadcast video effects systems were some of the first steps toward GPUs. According to Ken Kutaragi, Sony's $350,000 System-G 3D video effects hardware (which reportedly had worldwide sales of... three units) led to the Playstation GPU.

The Toaster effects could be interactive because it relied on the Amiga's graphics output as its address generator. In fact, the Amiga computer's monitor output was normally used to display the Toaster user interface but when a video effect was running the interface was entirely replaced with odd patterns that looked like bar codes. These were the addresses being generated by the Amiga custom chips and fed from the Amiga to the Toaster hardware in real-time via the monitor output (technically the fastest 'bus' in the system). This was a remarkable hack which required the Toaster to be very tightly coupled with the Amiga's hardware design and also involved some other extremely clever trade-offs. Relying on the Amiga's graphics output as the real-time address generator enabled the Toaster to exist and was also why the Toaster could never be ported to another computer or even to the PAL video standard. The Amiga's genlockability just allowed the Toaster to be even less expensive.