Yes, other countries have them. They're not willing to produce them at the higher cost required to obey environmental laws. I'm not sure how patent laws are a huge issue here: rare earths may have increasing market demand, but they've been extracted and processed for countless years. Only innovations China has made in the last ~20 years would be covered by patents. I'm sure there have been some innovations, but I'm also sure our other mining industries in the US would be happy to leverage their patent portfolio in a patent war if China wasn't willing to work on reasonable licensing terms.

A global strategic bottleneck in China for these things doesn't require patent or environmental law violations, it just requires us to pay more for them. For a critically strategic resource like this, the US should ensure a consistent supply chain independent of geopolitical concerns with China. And if China were to cut off supply then concern for their patents goes out the window too.