Why starlink? Planes typically use Inmarsat which provides better coverage.

Various aircraft data are already uploaded in flight ("stream" would be an exaggeration though) as you can see from the MH370 example you cited. The data uploaded are increasing as companies like Rolls-Royce become more of a data company.

The black boxes are pretty robust (assuming you can find them!) and uploading the voice data is probably not worth the cost.