Most likely answer to the OP's original question.
Long ago researcher was investigating LT runs and did a study with people running for 20 minutes. 20 minutes was picked cause it seemed like a reasonable number. They had to pick something after all. They could have picked 30. Or 23.5. Or 17.
Then the next researcher came along. They picked 20 minutes as well because that way they could compare their results with the first guy.
Repeat with many more papers. Along the way one or more of the papers came to the conclusion that this was a good workout. Conclusion:
LT run for 20 minutes is a good workout.
Of course none of this says anything about whether it's a *better* workout than a 19 minute or 21 minute run. Or even a 40 minute run somewhat slower.
Or what would happen if you ran them consistently as part of larger training program versus doing longer, slower threshold runs (as Malmo advises). It could very well be that the 20 minute LT run is a bigger stress (and therefore larger adapation stimulator) than the longer slower threshold, but that the typical runner can manage more volume of the slower runs over an extended period (without injury) and therefore the slower threshold run gives the better long-term payoff.
None of this is known 'scientifically'. Nor are the studies that would scientifically 'prove' either side of the issue likely to ever be done.
And most importantly even if we established somehow that the average runner benefited maximally from 20 minutes at LT it still doesn't help. It's clear that the range of responses across different individuals is large. So 20 minutes is unlikely to be best for *you* even if it is best for the average runner.
Hence the admonition to run by feel rather than by the numbers.
And I don't know about you, but to me a longer, slower, progressive threshold run feels like it's what my body was meant to be doing much more so than trying to stick exactly to LT pace for 20 minutes.