It depends.
A decision model can only be considered "useful" or not given a particular setting. You can see this in everyday life, where different decision processes result in a wide range of performance measures, from near-perfect to slightly-better-than-random. Take, for example, a few different decision processes, like 1) diagnosing a severe medical issue, 2) returning top search hits, and 3) selecting batches of parts for inspection. In each of these cases, one should conider the relative costs of false positives and negatives, and tune the decision process to optimize for the desired metric.
A medical screening test, for example, should have high recall, catching all true case of disease at the cost of some false diagnoses. A search engine, on the other hand, should have high precision, as it doesn't need to find every relevant webpage, but the ones it does return must be relevant. An industrial decision tool to direct parts inspectors may be useful even if it is only slightly better than random, as virtually any improvement makes the inspectors more efficient.
As you can see, there is not a numerical threshold for any performance measure that separates useful and non-useful models. It all depends on the context. A decision model with 30% precision may indeed be useful in some settings, but not others.