Resonant enhancement both in passive and active resonators is a well-known technique for boosting the efficiency of nonlinear frequency conversion at high repetition rates. However, this route has remained poorly explored for the generation of few-cycle broadband THz transients due to the inadequacy of typically employed nonlinear crystals. Here, we demonstrate that thin lithium niobate crystals are a promising candidate to circumvent current difficulties. Using a 50-µm thin lithium niobate plate intracavity of a compact high-power mode-locked thin-disk laser, we generate broadband THz pulses with a spectrum extending up to 3 THz at 44.8 MHz repetition rate, driven by 264 W of intracavity average power. This approach opens the door to efficient high-power single-cycle THz generation at high repetition rates, scalable to kilowatt-level driving power with low cost and complexity.