This sounds like a good idea. But, it may not be possible in most of the hard sciences. Imagine writing an 800-word layman's summary for some results in string theory.
By 'most of the hard sciences', you seem to have chosen a sliver of one of the hard sciences, which plenty of people in that science think is just smoke and mirrors. If a 'general audience abstract' is a good idea, it shouldn't be balked at because of a single theoretical field which is quite controversial. Let other journals handle those papers :)
This week i read a headline that could be interpreted as saying green tea would prevent zika infections.
In reality it was a chemical of some sort found in green tea (and elsewhere) that seemed to counteract zika. But it required concentrations that you would never find in nature.