If the government passed laws/regulation that mandated certain packaging requirements for companies like Coca Cola, that would be a top-down solution and Coca Cola would have to comply, lest they wish to face steep fines and litigation.
In regards to soda, you're right - consumption taxes have proven effective. I believe cigarette taxes have proven effective in the same way. But an environmentally effective top-down solution would of course apply to many more consumables that just soda, sugar cakes and other generally unhealthy items. It's possible that top down regulation could push costs higher for smaller companies that offer healthy options in environmentally unfriendly packages. If costs are too high for smaller companies like these, then there may be fewer healthy alternative options (because we know Little Debbie and Coca Cola aren't going anywhere, regulations or not). This is obviously a very generalized example - in reality, many of the healthy/organic foods items already come in environmentally-friendly packaging.
If people start having to pay for garbage processing by weight or volume, people would change their tune pretty quickly, in the same fashion that instituting small charges on bottles and cans boost recycling of those products.
The downside is that those that are charged directly often dump wherever they won't be caught. Example: mattresses, they're a dumping problem, often, bulk items are even included in curbside pickup with the minium effort of scheduling a pickup.
Other than that, I do think some level of optimizations should happen in the space of recycling... either similar to what I understand German regulations are on recycling what you produce... and/or going back to glass bottles.
Then again, I'm not sure how bad plastics are in general, other than what gets dumped into the oceans, for the most part, my understanding is plastics in modern waste facilities aren't so bad and mfg is mostly a petroleum byproduct of what would otherwise be waste anyway.