Sure, I won't object if you have a few mines for rare earths, if you stop deforestation for cattle feed (90%) and deforestation for cheap metals (iron etc - which is the other 10%). 1% for rare earths would be fine tbh. However this is not why the rainforest is being cut down. It's being cut down so that people can eat beef multiple times per week (with the resulting public health crisis that will come from that).

You say that as though the Amazon is the only place on earth rich in rare earth minerals. It isn't - many places have them, a number have more than the Amazon.

Rare earths are not rare - the 'free minerals' are rare (non existent) to find "just laying about" as they bind to other elements and compounds in complex hard to unbind ways.

What the planet is rather short of is good, high quality, original condition rain forests.