Browser fingerprinting works best against people with unique headers. There's probably millions of people using an untouched safari on iPhone. Once you touch your user-agent header, you're likely the only person in the world with that fingerprint.
Unless you've got some superintelligence hidden somewhere, you'd choose a neural net. To train, you need a large supply of LABELED data. Seems like a challenge to build that dataset; after all, we have no scalable method for classifying as of yet.
Because servers would serve different content based on user agent virtually all browsers start with Mozilla/5.0...