Hollow-core waveguides are central to advancing low-loss, high-speed light transmission, and tailored beam delivery in modern photonics. In this study, we reveal that the fundamental mode of such waveguides shows intrinsic focus-like light concentration when coupling out to free space, without requiring any external optics, arising solely from the non-Gaussian nature of leaky modes. Through detailed experiments and simulations, we investigate this phenomenon in both anti-resonant hollow-core fibers and air-silica capillaries, demonstrating that the focus-like light concentration behavior is a general feature of leaky waveguide systems. We further analyze its impact on inter-fiber coupling and establish its connection to the underlying mode structure. These insights deepen the understanding of leaky mode physics in complex waveguides and open new opportunities for structured light delivery, compact fiber coupling, and efficient optical interfacing in fiber-based and integrated photonic platforms.