Despite the growing calls to integrate realistic human behavior in sustainability science models, the representative rational agent prevails. This is especially problematic for climate change adaptation that relies on actions at various scales: from governments to individuals. Empirical evidence on individual adaptation to climate-induced hazards reveals diverse behavioral and social factors affecting economic considerations. Yet, implications of replacing the rational optimizer by realistic human behavior in nature-society systems models are poorly understood. Using an innovative evolutionary economic agent-based model we explore different framings regarding household adaptation behavior to floods, leveraging on behavioral data from a household survey in Miami, USA. We find that a representative rational agent significantly overestimates household adaptation diffusion and underestimates damages compared to boundedly rational behavior revealed from our survey. This "adaptation deficit" exhibited by a population of empirically informed agents is explained primarily by diverse "soft" adaptation constraints-awareness, social influences-rather than heterogeneity in financial constraints. Besides initial inequality disproportionally impacting low/medium adaptive capacity households post-flood, our findings suggest that even under a nearly complete adaptation diffusion, adaptation benefits are uneven, with late or less-efficient actions locking households to a path of higher damages, further exacerbating inequalities. Our exploratory modeling reveals that behavioral assumptions shape the uncertainty of physical factors, like exposure and objective effectiveness of flood-proofing measures, traditionally considered crucial in risk assessments. This unique combination of methods facilitates the assessment of cumulative and distributional effects of boundedly rational behavior essential for designing tailored climate adaptation policies, and for equitable sustainability transitions in general.