Status of entanglement/black hole entropy in quantum field theory It used to be said that in QFT, black hole and entanglement entropy is overcounted because entropy turns out to depend on volume, even if we somehow eliminate infinities.
Does this assessment still remain true for quantum field theory? 
 A: In general if you study physical systems without taking gravity into account, the entropy scales as volume. Modelling such systems with QFT gives you the same conclusion, so there is no contradiction in this case (provided you can control divergences).
However if you take gravity into account, you can show that there is a bound on the entropy which is proportional to the area of the system under consideration, not the volume. In case of black holes, the entropy is given as
$$S = \dfrac{A}{4}.$$
Now say you want to calculate the entropy using a special case of scalar field on a Schwarzchild background*. A calculation of this type will give us much more entropy than we are actually looking for. It breaks the above mentioned entropy bound. Thus we say that we are over-counting the degrees of freedom in the calculation of the entropy.
Strominger and Vafa [1] were able to give a correct calculation of the entropy for $5D$ extremal black holes. The thing to note here is that they modelled their system using a string-theoretic construction, not a field-theoretic one, which enabled them to reach a correct conclusion.
[1] https://arxiv.org/abs/hep-th/9601029
* You need to be careful in this type of calculation. Naively if you might think that spacelike separated scalar field operators are independent. Turns out that this locality based argument doesn't hold in gravity. Looking at resolution of no-cloning paradox and strong-subadditivity paradox, you realise that operators in the black-hole interior are a "scrambled" version of exterior operators.
