This paper investigates reconfigurable intelligent surface (RIS)-assisted wireless communications under a two-timescale architecture, in which the RIS phase shifts are optimized from long-term channel statistics, eliminating per-element training and thereby slashing channel estimation overhead. It is shown that, while the power captured by the RIS scales linearly with the number of its elements, the two-timescale beamforming gain upon re-radiation towards the receiver saturates rapidly as the number of RIS elements increases, for a broad class of power angular spectra (PAS). The saturation ceiling depends on the PAS angular decay, which governs how quickly inter-element spatial correlation vanishes. Steeper decays yield stronger correlations and, hence, a higher ceiling. The implications of this saturation on the effectiveness of two-timescale RIS-assisted communications are discussed.