The Process Stream class does not support writing

Yes, because it's the output of the other process. You're only able to read from it. From the documentation.

Gets a stream used to read the output of the application.

I know it's a bit confusing, but think of it as StandardOutput from the perspective of the process. (Not from your perspective, as another process looking at it.)

If you want to write data for the other process to read, you'd use Process.StandardInput instead.