Leveraging demand-side flexibility resources (e.g., buildings) is a crucial and cost-effective strategy for addressing the operational and infrastructure-related challenges in power grids pursuing deep decarbonization with high renewable energy penetration. However, the demand flexibility opportunities and financial benefits for residential space heating, which are sizeable demand-side flexibility resources, through emerging building energy management solutions (i.e., smart control and phased change material (PCM) thermal storage) across the US are not fully understood. In this paper, we systematically assess the demand flexibility and cost-saving/revenue potentials in residential space heating through detailed building-level simulations for five consecutive years at a 5-min temporal resolution in 20 metro areas across the high-heating-demand regions of the US. The results show a high degree of synergy between PCM thermal storage and smart control, which enables substantial demand flexibility potential, reaching 98.5% of peak load shifting, and electricity cost-saving/revenue potential, reaching 338.3% of electricity cost reductions, for residential space heating in the US. By achieving such performance, adopting smart control and PCM thermal storage is financially viable in 50% of the tested metro areas. The results reveal that the demand flexibility and cost-saving/revenue potentials of residential space heating in the US are further enhanced by higher volatilities in electricity prices. Active PCM thermal storage has lower energy efficiency but much higher energy flexibility than passive PCM thermal storage. Based on the findings, recommendations for integrating PCM thermal storage and smart control systems within residential space heating are provided.