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Tax exemption implicitly subsidises the (sometimes foolish) donations of (mostly rich) private donors
This argument seems to frame 'not paying as much tax' as 'taking from (other) taxpayers/society" which seems to presuppose the moral legitimacy of taxation in a very strong (and controversial) way.
From a consequentialist point of view, this is only "bad" if the expected social value of private donations is lower than the expected social value of tax revenue
This is hard to assess, but my (Gus) hunch is that private donations are more socially impactful at the margin than government spending
Tax exemptions create legal complexity and distort incentives (e.g. big 4 have tax minimisation service lines which is a waste of money and talent). Getting rid of all tax exemptions is a good idea, and removing the charity exemption is a step in this direction.
You need to be careful of the theory of the second best. Whether this policy is good at the margin should be considered independently.