In light of this answer, why do we say V'imru amen and V'nomar amen at various points in bentching and davening when saying that passage alone? (eg. bentching by yourself, or oseh shalom at the end of one's silent amida) It sounds like these phrases were instituted for scenarios with group participation.
I would think that it is better, if possible, to incorporate group participation for these things as much as possible. However, even alone, one says "ואמרו אמן" and the like. Why? I will quote R' Yaakov Emden (regarding the phrase said at the end of the Amida to conclude "Elokai N'tzor"), but do not assume that I know what he means:
.ואמרו אמן - אף ביחיד אומרו. כלפי המלאכים המלוים אותו
literally: "And say ye amen": even in solitude he says it, toward the angels/messengers who are escorting him.
EDIT: I just found this P'ri Megadim (EA 189:1) who writes (regarding the conclusion of the Harachaman section in Birkas Hamazon) that when alone, one should not recite "ואמרו אמן" or "ונאמר אמן", but rather just "אמן". [It looks like most siddurim don't follow this, though.]