Hopes for climate progress have increasingly rested on generational change — the expectation that younger, more environmentally conscious generations will consume less and emit less than their predecessors. Here we show, using data from approximately 2.8 million individuals across more than 40 countries over three decades, that this expectation is empirically unfounded. Despite expressing substantially stronger concern about climate change, younger generations maintain household carbon footprints that are comparable to or higher than those of older generations at equivalent life stages. This divergence is not explained by weak preferences or hypocrisy. Rather, it reflects the fact that the large majority of household emissions are structurally embedded in energy grids, transport systems, and global supply chains that individuals cannot alter through consumer choice alone. Where these structural constraints are tightest, the gap between concern and emissions is largest; where they are weakest, the gap narrows. These findings reframe a foundational assumption of climate policy: that changing minds will change emissions. Individual agency over carbon outcomes is far more constrained than policy discourse assumes, and generational change in attitudes — however genuine — cannot substitute for the structural transformation of energy and production systems.