This paper examines whether the planetary and environmental costs of contemporary artificial intelligence transformation is beginning to outweigh its promised contributions to climate mitigation and environmental sustainability. It first surveys constructive uses of AI, including applications in climate modelling, energy system optimisation, natural capital accounting and precision agriculture. It then analyses the material footprint of AI across the full life cycle of systems and infrastructure, from mineral extraction and semiconductor fabrication to model training, inference, data centre construction and end of life disposal. The analysis highlights the steep growth in electricity demand, greenhouse gas emissions, pollution and freshwater use associated with large scale model training and generative AI services, as well as the concentration of new data centres in regions already experiencing water stress. It argues that current governance, which relies largely on voluntary corporate disclosure, market based instruments and fragmented national regulation, is inadequate in the context of accelerating investment and an emerging international AI arms race. In response, the paper examines various governance approaches, from pre-deployment planetary, environmental and health impact assessments, standardised life cycle reporting for AI infrastructure, and sustainability by design requirements, to more innovative mechanisms aimed at democratising control over computational resources by prioritising public interest use cases, including the establishment of public interest consumption thresholds and the reservation of accelerator capacity for independently certified AI for Good applications. The paper concludes that a benefit sensitive and climate conscious governance framework is needed to ensure that AI development realises its genuine contributions to societies, including climate mitigation and environmental protection, while remaining compatible with planetary boundaries, resource justice and intergenerational equity. Such a framework should also encourage policymakers to ask, for each use case and major application of AI, whether it is in fact worth its planetary costs.