Why do we use so much plastic, and what could (should?) replace it?

There are already, viable replacements; depending on the item to be contained. Many of products are sold in them already. Polymer blends made from plan fibers that are engineered to start decomposing once the come into prolonged contact with soil. The common customer just doesn't know it. Companies don't use it as a marketing tool because many consumers would falsely believe that the packaging will decompose on the shelf. They have half-lives that are measured in months and are essentially "gone" 1-2 years after being put in a land fill. The disadvantage is that they typically won't take as much abuse as plastic containers.

The most difficult and thus expensive packaging problem are liquids and oily solids. Americans like their soft drinks in clear containers. There are decomposing translucent containers and their half lives are measured in years or decades, taking 50-100 years to "disappear" and they aren't cheap. Compressed wax paper containers or foil lined paper containers are viable, but test marketing has shown that Americans typically will stop using a product that switches to them, favoring plastic.

By the way polished paper finishes with a high gloss print labeling adds years onto the half life of paper packaging.

Recycle is an alternative but just maybe reducing the production of some of these products and use safer alternatives. But that costs money and getting Corporations to spend money protecting the environment seems difficult in today's market place.

Supposedly it's cheaper to make, need to either recycle more of it or find an alternative material that is cheap, and biodegradable.