In most cases, the approval of pharmaceuticals is subject to strict regulations. The evidence required for this often refers to the measurement methods established at the time of approval. These measurement methods are usually validated, i.e. statistically verified by a large number of repeat measurements. Technical advances in analytics often generate faster, more accurate or better automated methods, which then also have to be validated. In order to establish such a method in the official drug books, the methods are then reviewed again. All this takes a lot of time and money, so it does not surprise me that many "old" methods continue to be used.
In some cases, the "more modern" methods are certainly used for routine and only in critical cases the official method is used as a reference.
Apart from that, a classical wet chemical method does not necessarily have to be worse or less accurate than a modern instrument-based method. These methods are often not very automated and not suitable for high throughput.
Joachim Horst gave you a good explanation. I would add that classical analytical methods are often more precise - not more accurate - than modern methods since you just measure weight and volume. In modern methods, you still measure weight and volume but you have to add the uncertainty of the instrument. Thus, the overall uncertainty - standard deviation - of classical methods is usually lower than modern methods. The accuracy can be the same since you calibrate with reliable standards. However, detection limits and speed are much better in modern methods.
I would add to the above answers that the methods contained in the Pharmacopoeias should also be as simple as possible and easy to reproduce by other laboratories. In this sense, it would be much more difficult to recreate 100% analytical setups involving complex, expensive and multi-component techniques requiring specially trained personnel.