Soft robotics is gaining interest in rehabilitation applications, bringing new opportunities to offset the loss of upper limb motor function following neurological, neuromuscular, or traumatic injuries. Unlike conventional rigid robotics, the added softness in linkages or joints promises to make rehabilitation robots compliant, which translates into higher levels of safety, comfort, usability, and portability, opening the door for these rehabilitation technologies to be used in daily life. While several reviews documented the different technical implementations of soft rehabilitation robots, it is essential to discuss the growing clinical evidence on the feasibility and effectiveness of using this technology for rehabilitative and assistive purposes, whether softness brings the expected advantages from the perspective of end users, and how we should proceed in the future of this field. In this perspective article, we present recent clinical evidence on how 13 different upper limb devices were used in both controlled (clinical) and uncontrolled (at home) settings in more than 37 clinical studies. From these findings and our own experience, we derive recommendations for future developers and end users regarding the design, application, and evaluation of soft robotics for upper limb rehabilitation and assistance.