How did you calculate those stopping distances?
Are they the ones taken from the highway code which are very out of date?
Yes it's the doubt distances from the Highway code, however I would disagree that's is out of date.
In highway engineering there's two stopping distances which are used this is how they compare with the highway code:
0.67 second reaction time, and braking force of 6.57m/s/s - highway code (23m at 30mph)
2 seconds reaction time and braking force of 2.45m/s/s - Design Manual for Roads and Bridges (70m at 30mph)
1.5 seconds reaction time and a braking force of 4.41m/s/s - Manual for Streets (40m.at 30mph)
Whilst most production cars can achieve 7.82m/s/s (0.8g) and so can stop (assuming a 0 second reaction time) in just 11.5m, you'd still need a reaction time off 0.86 seconds to still stop within the 23m cited in the highway code for 30mph.
Likewise at 20 you'd stop in 5.1m giving you a thinking time of 0.77 seconds to stop within the highway code 12m
That means that the amount of thinking time from being at 20mph is 2 seconds to achieve the same 23m stopping distance. That's still about a second more. At those speeds, the distance reduction from better braking isn't really all that much, given that the 30mph reaction time is still noticeable below 1 second.
As an example of we set the braking force at 5 times the force of gravity (which F1 cars can achieve, whist most production cars compare at 0.8 times the force of gravity) from 30mph you'd do this in 1.8m, add in 1 second for a reaction time and the total stopping distance would be 15m, now from 20mph with the same breaking force you would stop in 0.81m, leaving you with 1.6 second reaction time to still stop in the same 15m distance. Whilst the gap has closed from about 1 second to 0.6 of a second, the braking force is significantly better than what most road cars could achieve (for example airbags deploy at 2g). Even if the car was capable, in not sure that the road surface would allow you to reliability achieve it and you'd need new or nearly new tyres all the time
Therefore, even with better braking it's likely that in most circumstances someone travelling at 20mph has about an extra 1 second of reaction time compared to someone travelling at 30mph.