After you have spent your first emblem for each giant, it is worth keeping a collection of them. You can top up mood, energy and xp once every game day, and there are badges for colllecting so many.
We are told that second emblems will eventually be necessary to unlock new skills, so you may be happy to have a small collection of them. Personally, I have 47 of them in bags in my house, and I try to fondle them once per game day, giving me +1692 XP, +940 energy, and +1175 mood for very little effort.