I feel there might be some extent to which this could be motor and/or gearing related in addition to engineering/design goals. In this case, "gearing" refers to the planetary gears in the motor housing for a geared motor rather than the gears on the cassette/freewheel. Direct-drive motors have only as much torque as the actual electric drive system itself can provide, and different motor designs might have limits on starting torque, which if it is too small, will not even move the wheels. As a result, they will try to apply an initial burst at higher voltage to get things moving only to scale it back once there is some actual movement. This is akin to how fans (which also have very low torque direct-drive motors) will start up with high torque first; it's also why fans have "high" as the very first setting after "off." For geared motors, you don't necessarily have that same torque issue because the planetary gearset will give you some torque multiplication. However, the core motor RPM has to be higher since there's a step-down gearing in effect. That multiplier not only affects getting up to speed from a stop, but also accelerating since a, say, 2:1 gearing ratio means double the absolute core RPM difference for the same absolute speed difference vs. a direct-drive setup. Since it would normally take longer to get up to that higher RPM for a given power input, that could give a feel of a laggy response, which is potentially undesirable. To counteract this, firmware programmers will probably just boost the voltage during acceleration so that the "revving" up and down can happen more quickly and response feels immediate.
Also worth noting is that bikes, AFAIK, don't really have a true weight sensor, so they will provide whatever starting torque/power output they need for the upper limit spec'ed mass of bike + rider. So if a bike is spec'ed to carry up to a 275 lb rider (which in engineering-land really means that 325 lbs is safe, but not recommended), and a 130 lb rider gets on that bike, that motor controller is going to accelerate at a level fit for roughly double the overall weight. Now in principle, a torque sensor can negate this since a lighter-weight rider is likely to also put less strain on the crank than a heavier one, so you get a mock weight-based scaling effect that way.
A pain point of cadence sensors is that the need for immediate response is quite possibly what becomes a limiting factor in how smooth they will be. A person's instantaneous pedaling cadence is naturally uneven through the cycle, but in order to respond quickly, they will measure your cadence as soon as possible and just roll with it. If you wait for a full cycle at least, you can use the "average" cadence to get something more accurate, but again, you get a delayed onset of power that people might find too laggy. You could also scale the estimated cadence according to the specific angle since the amount of force people can apply through the pedal stroke is pretty predictable, but you'd need some sort of crank position sensor. Whatever the case, different companies will prioritize the quick response vs. smoothness balance differently and different models of motors will have different gearing ratios and so on.