Fingerprinting concerns here are really overblown. At least in Chrome's implementation, the model version / responses will give you ~2 bits over the browser major version: whether the machine can support the model, and whether the model is downloaded yet or not. (Really <2 bits, since these ratios aren't 50/50 in the population.)
This is discussed in detail in https://webmachinelearning.github.io/writing-assistance-apis....