A Gaussian seeing/optics blur crushes high spatial frequencies. Noise doesn't fall off — it's flat across frequency. Deconvolution scales both back up by 1/MTF, so the frequencies you "gain" by sampling finer come back as noise. Drive the sampling and watch the Nyquist line walk into the dead zone.
Blue: how much of each frequency survives the blur. Amber: the gain deconvolution must apply to undo it (1/MTF) — which is exactly the noise amplification at that frequency.
A dim background at your target SNR, blurred and sampled, then naively deconvolved to Nyquist. The signal is "restored" — and so is a much bigger pile of noise.