Don’t seats that recline flat defeat the purpose of having seatbelts?
I'm not sure that comparing car seatbelts to airplane seatbelts is that useful here. The acceleration involved in a car crash at highway speeds are much greater than even the acceleration, mostly vertical, involved in even severe turbulence. 

For example, after a 2015 severe turbulence encounter, investigators determined: "In the first event, the peak vertical acceleration forces recorded were + 1.7 and + 0.14 g. In the second event, peak vertical acceleration forces recorded were + 2.21 g and −1.32 g," not that much greater than the kind of acceleration you might feel in a car if you drive really aggressively. That's enough to throw unrestrained passengers and objects about (just as if you slam on the brakes in a car), resulting in injury, but it's a much smaller acceleration than what you'd see in a 30mph car crash. Nobody would consider being slammed against their seat belt like that, whether they're seated upright or reclined, to be enjoyable, but it beats slamming your head into the ceiling. 

Forces much larger than that exceed the design load limits required for the aircraft, and once you're beyond that and the required safety factor, your biggest worry is the structural integrity of the aircraft, and you're less concerned about whether people's limbs flailed about.

In the case of an actual crash (such as the 16g standard new airplane seats are tested to), lying flat could pose a much larger risk of injury, but that's beyond the design specifications of the seat, which are tested with test dummies in a normal upright position. There aren't a lot of survivable crashes that occur without warning during the cruise phase of flight (page 22). 

Car seats can also be reclined, and the diagrams the NHSTA produced of the results of crashes in those cases (see, for instance, page 41) are remarkably similar to yours. This is why "bring your seat to the upright position for landing" is a standard requirement.