Why are regenerative brakes uncommon on e-bikes? Few electric bicycles have regenerative braking. Most quality e-bikes seem to be settling on mid-drive, which even makes regenerative braking impossible because there is a freewheel between the wheel and the drive, and the rear derailleur as the chain tensioner!
Why is this the case?  Why are regenerative brakes rare?
There are several reasons for regenerative brakes not being common on bicycles unlike in electric cars:

Electric bicycles have very poor acceleration, and the rider produces about half of the acceleration with the motor producing the rest. The power is limited by the low-speed motor, not the battery. Most quality electric motors like to spin at 5000 - 20000 RPM, but in e-bikes they do not spin at any such speed range. The best RPM situation in electric bikes is in mid-drive bikes that have enough space to use reduction gears, and the mid-drive arrangement does not allow regenerative braking due to the freewheel. The worst RPM situation in electric bikes (lowest RPM) is in hub motors, the only arrangement that would make regenerative braking possible. These hub motors cannot produce high forwards torque, and therefore, cannot produce high inverse torque for braking. In contrast, electric cars are well-known for their high acceleration, thus allowing rapid braking. An electric bicycle with regenerative braking could produce only half of its poor acceleration as braking force, and it is not at all significant.

A common use case for regenerative braking in electric cars is going downhill. Most car drivers drive always very near the speed limit (unless traffic condition or safety requires otherwise). In contrast, most bicyclists ride at a very low speed that could be much higher. A car driver going downhill needs to brake to keep under the speed limit, whereas a bicyclist often uses a downhill as an opportunity for going fast. The most common braking at downhills for bicyclists is a 90-degree or hairpin turn after a downhill, and to maximize average speed, most bicyclists only brake very close to the turn, instead of braking all the time before the turn. Thus, a downhill is not a good location for an electric bicyclist to brake.

Another common use case for regenerative braking in electric cars is stopping at a red light. In contrast to cars where braking close to red lights instead of anticipating the traffic lights far away is common even for internal combustion engine cars lacking regenerative braking, most bicyclists have learned an energy-saving way of going through traffic lights, avoiding unnecessary accelerations to high speeds only to need to brake right away. While a regenerative brake could be useful for an electric bicyclist adopting a different rapid start - rapid stop riding style, most bicyclists do not consider such a riding style necessary.

The final killing blow making regenerative braking infeasible is the controlling of such brakes. In most cars, there is natural engine braking. Some electric or hybrid-electric cars (Toyota) simulate the typical engine braking amount with regenerative braking, while at the same time having complicated (expensive, heavy) machinery to adapt between regenerative braking and disc braking using the brake pedal. This approach has the advantage of familiarity for most automatic transmission car drivers. Such an expensive, complicated and heavy machine would not be acceptable on a bicycle. Other electric cars (Tesla) cheat somewhat and make the engine braking huge, to avoid having the complicated (expensive, heavy) machinery to adapt between regenerative braking and disc braking when the driver presses the brake pedal. In contrast, high-quality bicycles have extremely low rolling resistance and no engine braking -- there is a freewheel. The natural slight regenerative braking would be of no value in such a bicycle. The braking controls of a high-quality bicycle are independent levers for front and rear wheels. A regenerative brake would work on only one of those levers. Most of the time, the bicyclist uses the front brake only, and most quality hub motor electric bicycles are not front wheel drive for a good reason (when going uphill seated, the front wheel is practically unloaded and would slip). Even for a bicyclist that brakes with the rear brake, there would need to be complicated (expensive, heavy) machine to operate both the regenerative brake and the disc/rim brake with the same lever. Cyclists would not find such a piece of machinery acceptable. Thus, the only way to make regenerative braking possible would be to add a third regenerative brake only control working only for the rear brake. It would be a terrible brake due to the low torque of hub motor drive. Such a brake would be unused for most of the time.


Also, to produce useful torque at low weight, an electric motor needs to spin fast. The only arrangement making the drive motor spin fast on an e-bike is mid-drive, where the motor drives the bottom bracket through reduction gears. Such an arrangement does not work with regenerative brakes due to rear derailleur being the chain tensioner, and due to the freewheel in the rear wheel.
Because regenerative brakes have terribly low power (reason #1), no valid use case (reasons #2 and #3) and no feasible means of control (reason #4), and because mid-drive is the most logical drive variant in e-bikes that makes regenerative braking impossible, regenerative brakes are not feasible on e-bikes unlike they are in electric cars.