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.
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.
Burning the plastic for energy is also generally better than landfill, though that might change if we otherwise have a 100% renewable grid since it would no longer be displacing dirtier fossil fuels.
There's actual science I could link to but I'll just point out one obvious red flag that gets repeated a lot:
If you wash the plastic in water heated with electricity generated from coal as part of the recyclong process then it's got a worse carbon footprint than not recycling it.
Apparent solution proposed by the people who use this factoid: stop recycling plastic.
Solution for anyone not under the sway of the fossil fuel industry: stop burning coal for electricity.
Basically everything is bad for the environment if you use coal powered electricity to do it. Coal sucks as an electricity source.
edit to add actual science:
Bernardo, C. A., Simões, C. L., & Pinto, L. M. C. (2016, October). Environmental and economic life cycle analysis of plastic waste management options. A review. In AIP Conference Proceedings (Vol. 1779, No. 1, p. 140001). AIP Publishing. Available at: https://aip.scitation.org/doi/pdf/10.1063/1.4965581.