One issue mentioned by NYT is using DAFs to "obscure their political activity" since donations don't have to be made public and non-profits don't have to disclose donors.
Another issue is that the tax savings felt by the donors is tied to the original contribution's valuation and not the valuation at the time the money is used. So in the case of GoPro's Nicholas Woodman, he got a tax break based on $500 mil, but the shares have dropped around 93% so if they're used for charity now it's like he only donated a fraction of that amount.
NYT also reports that the fees for some of these DAFs can be significant and so a portion of these donations are going to e.g. Goldman Sachs, Fidelity, and similar firms.