Have to tell the Nest thermostat to either cool or heat the house

I just moved into a house with a Nest thermostat and this is the first time I've ever had a thermostat of any kind (just had window units and radiators for the past 20 years).

I don't understand why I have to choose between heating and cooling modes. Isn't the point of a thermostat that I tell it what temperature I want the house to be, and it makes it happen (e.g. if I want it to be 70 and it's currently 75 then it cools, but if it's 65, then it heats)?

So, say it's a hot (85) and a cool (50) night – at 1pm I come home, and the house is 75 degrees so I set it to cool with a temperature of 70. I go to sleep, the temperature drops, and once it drops below 70 it can never go back up because it's set to "cool." So when I wake up, the house temperature is 60.
Note – this hasn't happened (yet, because the temperature swings aren't that extreme), but could it?