The author doesn't actually say taxing wealth is bad, just that it's not the panacea some might imagine it to be.
I think there's something of a missing point in this article - the author points out that much of the richest people's wealth is illusory, but the corollary here is that if taxing wealth reduced their apparent wealth, that would probably be a good thing since it would mean the value of their stocks would be more accurately defined, and it's definitely better to have lower but more accurate stock valuations, it's even worth reducing the actual value of the stocks somewhat.
If the author would have emphasized your conclusion, that taxing wealth would actually normalize asset values and bring them closer to reality, I would have agreed he wasn't against taxing wealth. But when this conclusion is somewhat implied but ignored, I'm assuming it's on purpose.
I think there's something of a missing point in this article - the author points out that much of the richest people's wealth is illusory, but the corollary here is that if taxing wealth reduced their apparent wealth, that would probably be a good thing since it would mean the value of their stocks would be more accurately defined, and it's definitely better to have lower but more accurate stock valuations, it's even worth reducing the actual value of the stocks somewhat.