We learn that once the meal is considered to have been concluded, one is prohibited from eating any longer until he recites birchas hamazon. Rashi makes it clear that he cannot eat even if he should choose to make a new bracha. What is the essence of this prohibition?
The Gemara differentiates between covering oneself when facing the public, on account of modesty, whereas on his way down to the river that is not allowed. Since the concept of tznius doesn’t necessarily depend on presence of other people, but rather on Hashem’s presence (See Shulchan Aruch O”Ch 2,2); if there indeed seems to be a tznius concern here, why wouldn’t this apply in any circumstance?