Another What if?

[Joseph_21sv]

Remember when home computers and video game consoles had to connect to TVs through the antenna jack and how they had RF modulators the purpose of which was to simulate a TV broadcast of the video (and audio) signals generated by those home computers and video game consoles and how this made the visual display so noisy? Anyway, after RF modulators largely became less relevant, there was effectively no longer a way to generate noisy video from these systems (Who would intentionally choose the inferior AV connection for a general purpose?). And this did not really make sense, at least through the 16-bit era, as most sound chips of the time did have a noise generator built in.
But what if the video hardware of the systems of those times also provided for a logical noise channel to be mixed with its physical video channel(s) as would have made design sense? Although it is probably obvious to you what this feature might have been used for once programmers discovered it and which systems might have been most likely to include it in an alternate timeline, what is not at all so obvious is what exactly might have been the details of the various implementations of it.