Recently, strong reduction of the quasiparticle peaks and pronounced incoherent structures have been observed in the photoemission spectra of layered cobaltates. Surprisingly, these many-body effects are found to increase near the band insulator regime. We explain these unexpected observations in terms of a novel spin-polaron model for CoO_2 planes which is based on a fact of the spin-state quasidegeneracy of Co^{3+} ions in oxides. Scattering of the photoholes on spin-state fluctuations suppresses their coherent motion. The observed ``peak-dip-hump type lineshapes are well reproduced by the theory.
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