Why do we fasten seatbelts for turbulence?

If you look at the FAA definition for turbulence intensity, you will see that you are probably only imagining Light turbulence, and perhaps occasional moderate. Severe and Extreme turbulence are very different from that.
Severe: Turbulence that causes large, abrupt changes in altitude and/or attitude. It usually causes large variations in indicated airspeed. Aircraft may be momentarily out of control.
Occupants are forced violently against seat belts or shoulder straps. Unsecured objects are tossed about. Food service and walking are impossible.

Extreme: Turbulence in which the aircraft is violently tossed about and is practically impossible to control. It may causes structural damage. Report as Extreme Turbulence.

Source is the FAA definitions of turbulence intensity:
Turbulence Intensity

As a cabin crew member, I have first hand experiences with real turbulence, both anticipated and unanticipated. The story of asking passengers to fasten seatbelts is not about people being thrown off their seats only, here are the reasons:

Flying people

Passengers and crew can literally fly around the cabin in real turbulence causing injuries not only to themselves but to other passengers who are sitting and buckled up. A few years ago I had a sudden serious turbulence over the Gulf of Bengal and I was with a few other crew members at the back galley having our meal after we finished the service, two of us hit the ceiling! it was B777 wide body and the ceiling is quite high, luckily none of us was seriously injured. When we went out to the aisle to check passengers, Many of them who didn’t fastened the seatbelt were literally on top of other passengers in other rows because of the turbulence, none was seriously injured but there was a big potential for that.

The seatbelt sign was off when it happened, but that’s not an excuse, in that specific airline as in many others, the seatbelt rules are "fasten your seatbelt when the seatbelt sign is illuminated, or while seated at all times". Seatbelts are actually meant to be fastened at all times, except when you really have to move (toilet, etc.). Anyway, crew members are the usual victims in turbulence since most of them would be standing and closer to the ceiling. I know some colleagues who had serious injuries that almost caused them disabilities.

So, to sum that up, seatbelts are really important in preventing some turbulence related injuries.

Making it easy for the crew

When there is light turbulence or bumping, even if the pilots know for a fact it is light and would never cause any one to be flying around the cabin, they need to put the sign on just to make things easier for the crew to move around, especially if it is during service time. In flights with hyperactive passengers, crew sometimes put the seatbelt sign on just to make people sit for the same reason. Turbulence will be the excuse here, but in reality, it is not a danger and the proof for that is seeing the crew in the aisle with carts serving people 😉

Again, airline pilots tend to put their airlines in the safe side, so the lightest possible sign of a turbulence will be taken seriously and people would be asked to put their seatbelts on so insurance companies can cooperate better.

You have a hard time imagining it but it exists. Sure, the plane won’t get flipped upside down but people have died as a result of injuries sustained in turbulence. For example, United flight 826 from Tokyo to Honolulu hit turbulence on 28th December 1997 just after being warned by other planes of extreme turbulence in the area. A few seconds after the seatbelt sign was switched on, the plane dropped 100ft, injuring 18 people, one of whom later died.

This Daily Mail article includes photographs of the mess in the cabin after a turbulence incident that broke bones and hospitalized four people.

I know someone who was unfortunate enough to be sitting on the TOILET when the seatbelt order was given. Soon afterwards he parted company with the seat as the plane dropped violently. He spent the rest of the episode using his ARMS to hold himself down.

Of courses, it’s in part to keep you in you seat when rare strong turbulences happen.

But it’s much more about getting your attention and orderly seating in the much more frequent event of less strong trubulences.

Sure, it’s only irritating, or even funny – except for the three old ladys over there on their first flight – It’s useful to have the people seated to get there really quick to calm the three down…

You’re fortunate enough to have never hit really bad turbulence. Although injuries from turbulence are rare they do happen. And from the FAA page:

Why is it important to follow these safety regulations? Consider this:

• In nonfatal accidents, in-flight turbulence is the leading cause of injuries to airline passengers and flight attendants.

• Each year, approximately 58 people in the United States are injured by turbulence while not wearing their seat belts.

So the statistics are in your favor, but it’s really one of those things that’s not worth risking. Of course the standard shaking turbulence that most people have experienced isn’t that big a deal, but it is quite possible to hit a pocket of turbulent air and have the plane basically drop through it, easily enough to throw you out the seat and into the ceiling or something else.

I will note that a lot of turbulence injuries come from falling luggage or other things flying around the cabin, so the seat belt doesn’t really help with that.

You’re advised to keep your seat belt fastened all the time because turbulence is hard to predict and in particular clear air turbulence can’t be easily predicted or avoided.

There’s lots more, including personal anecdotes, over at askthepilot.com.

I have experienced bumps which were powerful and unexpected enough to hit a ceiling by the head if not the seatbelt. Happened when descending over an island in Pacific in a large aircraft. Seatbelts are definitely there for a reason.

To quote Wikipedia on Clear-Air Turbulence, under “Cases”:

Because aircraft move so quickly, they can experience sudden
unexpected accelerations or ‘bumps’ from turbulence, including CAT (as
they rapidly cross invisible bodies of air which are moving vertically
at many different speeds). Although the vast majority of cases of
turbulence are harmless, in rare extreme, cases cabin crew and
passengers on aircraft have been injured (and in a small number of
cases, killed, as in the case of a United Airlines Flight 826 on
December 28, 1997) when tossed around inside an aircraft cabin during
extreme turbulence. BOAC Flight 911 broke-up in flight in 1966 after
experiencing severe lee-wave turbulence just downwind of Mount Fuji,
Japan.

Although turbulence strong enough to cause injury is rare, it does happen and being in your seat and belted can protect you (not in the extreme case cited, of course).