What you're describing is mostly a failure of US commingled recycling system. Meanwhile most of EU countries successfully recycle about 90% of collected glass, collected in glass-only containers.

Making new glass can be an issue, as it typically uses sand, which is not very renewable and sand mining in many countries causes massive issues with flooding, droughts, sinking, black markets, even sand mafia!

No we should not landfill everything after a single use, or we will soon run out of reasonably accessible raw materials in suitable forms.