Financial accessibility is a fundamental prerequisite for social inclusion, independence, and economic participation. Yet, millions of individuals with disabilities—particularly those who are blind or have limited mobility—face significant challenges in accessing everyday banking services. Automated Teller Machines (ATMs), despite being critical touchpoints for financial independence, continue to present usability barriers rooted in their reliance on vision, fine motor skills, and inaccessible interface designs.The rapid advancement of artificial intelligence (AI), especially in the form of agentic, multimodal systems, offers transformative opportunities to dismantle these barriers. By combining speech technologies, computer vision, natural language understanding, haptic feedback, and secure edge-cloud hybrid architectures, AI systems can reimagine ATMs and public kiosks as universally accessible. This paper provides a comprehensive exploration of how AI-driven solutions can enable financial accessibility for blind and mobility-impaired populations. It reviews the current state of accessibility in banking, highlights technological breakthroughs in AI for assistive interaction, presents a synthesized framework for agentic AI-powered inclusive ATMs, and analyzes both the benefits and challenges of such approaches. The discussion further explores deployment strategies, ethical considerations, and a roadmap toward nationwide, inclusive financial ecosystems. The findings suggest that with careful design, AI has the potential to transform financial infrastructure into a universally accessible system, thus breaking persistent social and technological barriers.