Best TV/HDMI shield for building Modern 8 bit ATMega Computer

The generation of a PAL/NTSC video signal requires a specific relationship between the phase of the colour sub carrier and the frame/line synchronising signals (measured in nanoseconds).
It is hopeless to do that with a micro controller.

I don't think I understand what you mean. There are several tutorials available showing how to achieve this . (I agree the resolution and color depth is somewhat lacking.) Is there something I'm missing?

If you need a Pi Zero for any part of it why not use if for all of it? Why bother with Atmega chips and a very slow 16MHz?

Indeed, I couldn't agree more. I'd rather use only ATMega(-like) chips.
On the other hand the low cost of a Pi Zero ($5) is not achievable with several ATMega chips, voltage regulator, resistor etc. So from this perspective, making the system I propose, is pointless.

So why do I want to make this? For fun and learning about the interaction between chips with different functions. The limitations of a (16MHz) 8-bit system can also be more fun to program than a (1GHz) 32/64-bit system.