Why make things more complicated than they need to be?
The ubiquitous programmable thermostats do different things at night, in the morning, during the workday, and in the evening. The idea being that the temperature is allowed to drift when no one's home, but is brought back in line by the time someone is in the house again.
However they are a PITA to program (tiny cryptic LCD, 4 buttons) and basically useless if you don't follow a consistent daily routine on the weekdays. Nest's value proposition is to be smarter about when the house is actually occupied/going to be occupied. Also when you're traveling (or if you have it in a rarely-used property) you can remotely start the heat/AC when you're several hours away so that it's comfortable by the time you get there. I have none of these problems, so I don't have one, but they do solve a problem that some people really have.
In fact you will save money & energy with manual control because the heating will not turn on when it's cold but you are wearing enough layers.
1. Economic - it easily paid for itself in one summer by not running the A/C when no one is home. I have geofencing set up to do this automatically.
2. Comfort - my office/bedroom temperature is all I really care about as it's where I spend all my time. My thermostat was not wired to there, and temperatures fluctuated wildly in my office. Ecobee has remote sensors so that I can set the rooms I care about to the correct temperature.
Overall, it has certainly made my life a lot less complicated; I never have to touch the thermostat again to get comfortable in my office, and I save a lot of money too.
My energy bills dropped about 30% with the Nest.
It does a number of neat things to save money, including running the AC fan through the chilled ducts for a period of time after stopping the active cooling.
For a forgetful person like me, it's also very handy to be able to turn the house into vacation mode the day after I left for vacation.
So 60F is surely fine.
Anecdotally, I was once without central heat for three days in 0-20F, and nothing froze. The basement got down to 38.
I had two pipes freeze and burst after 3 days of freezing temperatures (first time anyone can remember being more than 24 hours below freezing). One was an outside faucet, properly protected and insulated. The other was frozen inside the slab, near the wall.
60 Fahrenheit is practically a comfortable day-long office temperature. It's a _long_ way from freezing.
And having the ability to change the temperature from my bed is nice too.
I don't really care for the "learning" feature but the 2 other features I find critical are 1) ability to schedule, and 2) remote control.
It's nothing you really need, but it's nice to have. I can program the temp to go 10 degrees lower overnight, and have the heat ramp up 30 minutes before we get up. I can have the blower run 15 minutes every hour without heat or cooling to make sure air circulates around the house. You could do that by hand but it would be more manual and cognitive work.
While I don't have a Nest, I put a similar timer on my water heater and saved a lot of money ($20/mo).
You could set two pairs of heating times, and control which (or both/none) were used. There was an override until the next set point.
This was 1980s stuff, or maybe even earlier.
The interface was far easier to use than any digital one I've seen.
It actually wasn't super intuitive (in cooling mode it inverted the sense of energy saving mode, if I recall correctly), but it was easy and never failed me once I set it up.
Doesn't make sense, unless you're willing to live with the potential failure of those functions...