Meeting the targets of climate change mitigation set by the Paris Agreement entails a huge transformation of the energy sector, as low- or no-carbon technologies must gradually substitute traditional, fossil-based technologies. In this perspective, the vast majority of energy analyses and scenarios project a fundamental role of Carbon Capture & Storage (CCS). However, uncertainty remains on the actual techno-economic feasibility of this technology: despite the considerable investment over the recent past, commercial maturity is yet to come. The main aim of this work is to evaluate the impacts of a progressively delayed deployment of CCS plants from a climate, energy, and economic perspective, focusing in particular on the power sector. This is carried out with the Integrated Assessment Model WITCH, exploring a wide set of long-term scenarios over mitigation targets ranging from 1.5°C to 4°C in terms of global temperature increase in 2100 with respect to the pre-industrial levels. The analysis shows that CCS will be a key mitigation option at a global level for carbon mitigation, achieving about 30% of the electricity mix in 2100 (with a homogeneous distribution across coal, gas, and biomass) if its deployment is unconstrained. If CCS deployment is delayed or forbidden, penetration cannot reach the optimal unconstrained level, resulting in a mix rearrangement, with a strong increase in renewables and, to a lesser extent, nuclear. The mitigation targets can be met, but policy costs without the implementation of CCS are from 35% to 72% higher than in the corresponding unconstrained scenarios.