We present a numerical analysis of the dynamics of high-power self-similar light pulses in a fiber laser with a saturable absorber based on carbon nanotubes (CNTs). This analysis allows us to identify lasing regimes in a CNT-mode-locked ytterbium-fiber laser enabling the generation of self-similar linearly chirped light pulses with an energy up to 330 nJ, which can be compressed to a 210-fs transform-limited pulse width through linear chirp compensation in a pulse compressor. We show that, for typical parameters of a fiber laser, the bandwidth and the minimum transform-limited pulse width of a self-similar laser output are primarily limited by the small modulation depth of a CNT absorber.