If you are then anaerobic digestion of separated food waste/organic material are far better (again both economically and environmentally) than throwing it all in a landfill and trying to capture the gas later (especially as there other valuable/harmful outputs too). And that's what every well run government in the world is doing, because they've done the sums.
It definitely takes less energy (and thus fossil fuels and thus carbon) to landfill a plastic bottle and make a new one or plastic bottle makers would be much more adamant to recycle. We can safely rely amoral corporations to do what's cheapest.
I'm not anti-recycling and can't imagine who even would be. I'm in favor of whatever reduces greenhouse gas emissions the most. I just think that the biggest problem in modern environmentalism is that they are optimizing for something that isn't much of a problem (landfills) at the expense of something that is (greenhouse gases) without even thinking about it. It's well-meaning, they just don't even know that certain materials and recycling programs are making that trade.
It's definitely not economical. Talk to someone who works in recycling today. China stopped accepting it and it's backing up. That doesn't happen to aluminum because aluminum is economical.
They also base their results on methane production. It's increasingly being captured for use as a fuel, and the EPA has required it of larger facilities for decades.
Moving away from fossil fuels is the obvious solution regardless, no argument there. If we did that, it practically wouldn't matter whether we recycled it or not.