Responsible AI (RAI) guidelines aim to ensure that AI systems respect democratic values. While a step in the right direction, they currently fail to impact practice. Our work discusses reasons for this lack of impact and clusters them into five areas: (1) the abstract nature of RAI guidelines, (2) the problem of selecting and reconciling values, (3) the difficulty of operationalising RAI success metrics, (4) the fragmentation of the AI pipeline, and (5) the lack of internal advocacy and accountability. Afterwards, we introduce a number of approaches to RAI from a range of disciplines, exploring their potential as solutions to the identified challenges. We anchor these solutions in practice through concrete examples, bridging the gap between the theoretical considerations of RAI and on-the-ground processes that currently shape how AI systems are built. Our work considers the socio-technical nature of RAI limitations and the resulting necessity of producing socio-technical solutions.