It may be better for the environment to sustainably harvest trees to produce cardboard then to recycle other paper products.
A lot of paper is coated in clays, waxes, or plastics, and many inks might make paper unsuitable for use in food grade products like pizza boxes, without heavy processing.
Shipping boxes, maybe. If the structural properties of the resulting board are OK.
But most post-consumer paper is unusable for one reason or another. Recycling of industrial packaging is a slightly different story.
So the paper does, eventually, go to the landfill and become sequestered in the typical fashion.
If you live in an area that collects material for industrial composting you should 100% put the grease coated parts of the cardboard in your compost collection bin.
[0] https://www.portland.gov/bps/garbage-recycling/compost-what-...
I'm not too sure on the details of how that is done, but I imagine it involves driving huge trucks into forests, cutting trees with machines, stripping and cutting the trees, and transporting wood to industrial areas.
It has to be more CO2 efficient to recycle.
Which are brown. You don't have to worry about the inks or "substandard" or whatever". And then the pizza boxes aren't re-recycled because of grease.
You suggest we stick to trees instead of recycle, "for paper". But the whole point of recycling is to turn paper into pizza boxes (and presumably also our Amazon shipping boxes, etc.).
It sounds like you're trying to argue against recycling paper... when the reality is it's a huge success, when you realize paper is recycled into cardboard.