It could be made harder, yes. This depends a lot on how the text is hidden and what kind of noise you use, though. Also, this would quite likely also impact legit usecases - you'll obscure intended text and details, as well.

It should be solved by smoothing the image to remove high frequencies that are close to the sampling rate, to avoid aliasing effects during downsampling.

The term to search for is Nyquist–Shannon sampling theorem.

This is a quite well understood part of digital signal processing.