Current aviation roadmaps predominantly rely on the replacement of fossil kerosene by alternative jet fuels to mitigate climate change, but the systemic impact of such energy transitions on other planetary boundaries remains unexplored. Here we fill this gap by integrating prospective life-cycle inventories within absolute environmental sustainability assessment. We find that the core climate change and biosphere integrity planetary boundaries are systematically transgressed, making these roadmaps unsustainable toward 2050. Lower energy demand brings aviation closer to its share of safe operating space, but air traffic needs to degrow by 8.6% yr-1 for additional planetary boundaries to be respected. Associated demand in energy, land, freshwater and CO2 capture is significant, with clear implication on the feasibility of these scenarios. Our results therefore show that, in order to achieve absolute sustainability, a rethinking of aviation governance is needed toward a systemic approach combining energy transition and demand-side measures.