Reasons why not to wear power armor:
1. Power armor is scary. Power armor is like walking around in full body armor with an assault rifle nowadays - it's going to prevent you from doing a lot of business, and probably will get the cops called on you. If you want to interact with someone in a non-violent way, wearing power armor is not the way to go.
2. Power armor is slow. If you want to move around fast, then you shouldn't be wearing a tank.
3. Power armor limits agility.
4. Power armor requires skilled maintenance.
5. Power armor requires fuel.
6. Power armor is large. If you're trying to fit into a doorway or crawl through a ventilation shaft, you may not be able to do so in power armor.
7. Power armor is heavy. When running around ruined buildings, the power armor may weight so much that you'll fall right through the floor.
8. Power armor is valuable. If raiders see a lone person running around in power armor, they would reasonably want to take said armor away.
9. Power armor is uncomfortable. Think about sitting in a furnace in the desert for hours or days on end.
10. Power armor is inconvenient. You have to get out of the whole thing to eat or use the bathroom, and it's probably not that great to sleep in.
It's unknown which, if any, of these reasons (or others) Bethesda is going to implement.
In short, there are plenty of reasons why a realistic soldier wouldn't always want to be wearing his power armor, even for missions where power armor is not required.