Completely disagree. Reducing waste, recycling waste, and re-using waste are some of the ways to address climate change. Saying modifying human activity/population is the only way to solve a problem is as extreme as saying climate change isn't real.
> No business is out there emitting methane for shits and giggles.
No one says this, you're reducing the broader point to a poor cliff-note. The point is that the incentives for businesses to better address their waste are not there. If all one gets for managing waste responsibly is a higher bill every month and a good feeling in their stomach, why would a proper capitalist businessperson do that in the short term?
My point was that the "capitalist" is not running that production line in isolation, it is the end consumer demand that drives that pipeline. So yes consumer demand is the ultimate source of all this.
Carbon tax is but a first step but it is necessary as it will force the actors to take action. As you correctly pointed out they have no "incentive" to do so right now.