Could the new Nearby feature actually hide rarer Pokémon from Sightings?
Theoretically, yes, you are right that this new implementation could hinder your ability to catch rarer Pokemon.
However, this is a beta feature and Niantic is specifically looking for feedback like what you have posted above. While there is not a way to disable this new Nearby implementation currently, you should definitely submit this feedback to Niantic so they can take it into account before they introduce this feature universally.
Here is the link for submitting a bug report.