One of the things in the article that really resonated with me was her comment about the "public authority and institutional accountability that comes from ordination." Both are important. Yes, I can talk about Jesus without being ordained. But when I do so as an ordained person, it comes out not just as my view but with the backing of a community of faith who have authorised me to speak about these things on their behalf. And, I am also held accountable. When I misspeak, when I get something wrong or when I say or do something harmful, there are structures and processes through which I can be corrected and, if need be, even removed from the role. Ways for the community of faith to make clear that they don't stand behind what I've said or done.
I've backed away from informal ministry opportunities that don't have that accountability at times, because it wasn't safe - for me or the other people concerned - that I operate without that support and safety net.
The meaning of ordination depends a bit on your denomination, but in general it's the process of authorising someone for ministry in or on behalf of the church into a particular role as "clergy."