No, SAFe is not Agile. It's no surprise that teams resist change given the extensive training required to become "SAFe certified." They've been taught to operate in a very particular manner, one that prioritizes dependable delivery over learning, course correction, and agility. The tasks that make teams really Agile necessitate planned flexibility. They ought to be focused on customer success rather than a preset set of features. They necessitate a constant process of discovery, which invariably leads to unanticipated course corrections.
Agile was designed with a small team of 10 or fewer individuals in mind. However, SAFe is an enterprise-wide Agile framework that isn't confined to small teams and helps businesses scale lean and Agile techniques.
SAFe works with Design Sprints.