I am pushed for time, but look, the issue isn't simply one of the combustion process and capture of gases compared to landfill (which I agree is a dreadful solution).
The process of making a product uses energy. There's the energy from getting the raw materials in the first place, and then the energy associated with manufacturing. Often it takes a lot more energy than you release in burning that product later as waste (paper products like newsprint being a good example).
The environmentally responsible question to ask is not simply 'does this process release lots of greenhouse gases into the atmosphere' but 'is incineration the best way to conserve that embodied energy that has been poured into products'?
In other words, we need to look at energy conservation across the whole lifecycle of a product, not simply at the burning technology itself.
And here is where high rates of recycling are a MUCH better idea than burning for most waste fractions. There is a wealth of evidence from study after study that suggests that burning paper is a bad way of recovering energy compared to recycling, for instance. There seems to be an increasing evidence base that recycling plastics conserves more energy than burning them. Etc. etc. etc.
This isn't just about the science, though - waste is a huge political issue. Incinerators are a very costly thing to build, and they come with all kinds of political strings attached - councils tend to be locked into contracts to supply the incineration plant with waste, which often reduces recycling rates in their area.