Encrypted HTTP/2 (h2) has been worldwide adopted since its official release in 2015. The major services over Internet use it to protect the user privacy against traffic interception. However, under the guise of privacy, one can hide the abnormal or even illegal use of a service. It has been demonstrated that machine learning algorithms combined with a proper set of features are still able to identify the incriminated traffic even when it is encrypted with h2. However, it can also be used to track normal service use and so endanger privacy of Internet users. Independently of the final objective, it is extremely important for a security practitioner to understand the efficiency of such a technique and its limit. No existing research has been achieved to assess how generic is it to be directly applicable to any service or website and how long an acceptable accuracy can be maintained. This paper addresses these challenges by defining an experimental methodology applied on more than 3000 different websites and also over four months continuously. The results highlight that an off-the-shelf machine-learning method to classify h2 traffic is applicable to many websites but a weekly training may be needed to keep the model accurate.