Biomass provides renewable carbon, which is more valuable than the energy in biomass itself for achieving stringent emissions targets. Excluding biomass from the European energy system increases energy system costs by 20% in a net-negative emissions scenario, similar to excluding wind power or electrolytic hydrogen. Policies limiting biomass (residue) use likely need to be accompanied by strong policies to support a greater deployment of clean electricity, electrolytic hydrogen and direct air capture to achieve European emissions targets. Carbon capture and bio-electrofuels can increase the value of biomass by enhancing biogenic carbon utilization, thereby moderating biomass demand. Bioenergy with carbon capture is more cost-competitive than direct air capture under a wide range of assumptions, which may inhibit direct air capture deployment unless targeted by policy.