It's really quite hard finding general articles about waste to energy that aren't written either by anti-burning groups or the groups doing the burning. This article talks in depth about UK burning rubbish, but basically concludes that the technology is on the way out as we move towards a more circular view of waste. One of the people they talked to said that waste to energy is burning resources. It's taking a wide range of components and turning them all into ash. The article also talks about Germany burning significant amounts of rubbish, so much so that they import a lot to keep their incinerators busy because better recycling means they don't have enough. It also says that this shows that it's not a time to invest in new facilities, rather it should start to be phased out.

I ended up turning to Google Scholar for more informaation.

This study looks at incineration in the US. It seems positive towards Waste to Energy incineration, but I can't help but get the sense they are comparing it to older versions of the same thing. It does point out though that in terms of greenhouse gas emissions, landfills produce methane and much of this escapes to the atmosphere even in landfills where methane capture is done. But in their conclusion they imply that natural gas is a more environmentally friendly way of generating electricity.

This study [PDF] is old (2002) but at that time quoted the US EPA sayings that waste to energy can "produce 2800 MW of electricity with less environmental impact that almost any other source of electricity". This probably isn't relevant to us now though, since 80% or more of our electricity comes from renewable sources, and that will hopefully grow over time. That study also talks about mercury emissions from landfills, since mercury evaporates into the air.

This one also concludes that waste to energy is a great alternative to fossil fuels.

My general feeling from this is:

• Waste to energy is sold as a electricity generating alternative, not just as a way to get rid of waste
• Therefore it mostly compared against fossil fuels, of which it is better than all except gas
• At the time of writing, over 80% of electricity in NZ is being generated from renewables, and over half of the remainder is from natural gas

So comparing it to fossil fuels doesn't seem helpful for us. Therefore we need to compare it as an alternative to landfill, and ignore the electricity aspect:

• Landfills emit all sorts of harmful things, including methane (which best case scenario is 75% captured), as well as mercury
• Incineration does not emit methane but basically converts 1 tonne of rubbish into 1 ton of CO2. However, other than approx 20% plastic content, most of the rest is carbon neutral (ish) because the carbon came from the atmosphere to start (organics - food waste, wood and paper, etc).
• But methane comes from the organics, other carbon content is a carbon sink (here's a journal article though I didn't read too close)
• So if only organics produce methane, which is 10x worse than CO2 but best case 75% is captured, then this is the equivalent of about 2.5x the same organic content being burned. But if 20% is plastic (that would otherwise be a carbon sink in a landfill) then incineration already has 25% more to start. Plus this site says methane only makes up 50% of landfill gas emissions. If we guess the rest is carbon dioxide (it won't all be) then we can guess that it's perhaps 50/50 organic compounds to CO2 and methane. So this pretty much brings us back to equivalent emissions.
• Incineration filters the air to remove harmful products to below regulated levels
• Our rubbish is filled with valuable resources. Burning it turns those resources into ash.
• The ash still goes to landfill - so it doesn't totally prevent the problems with landfill
• Incineration can be done within cities to save on fuel emissions (but this one isn't planned to be urban, so we can ignore)

So summarising the summary:

• Landfill and incineration probably produce broadly similar greenhouse gas levels
• Incineration makes resources unrecoverable, and contaminated ash still goes to landfill

And one unanswered question I still have:

• In the video linked in the OP they talk about washing the ash to "clean" it. What happens to the now contaminated water (or whatever they wash it with)?

Overall, in my view (after spending all evening researching this 😆) is that incineration is not a solution to the problem, and is instead something that is falling out of favour overseas. Instead we should focus on reducing waste going to landfill, and with the non-recyclables we should invest in technology to be able to recycle them properly so the resources can be reused.