Actually you might be overestimating the esteem the English held their archers. Granted there were laws in place to foster profiiency with the longbow. But that's simply cause it takes time to learn to use any bow, and a six foot bow with a larger draw weight even longer. They used them a lot because the longbowmen were commoners and came cheap. And the English crown around the time they use large numbers of longbows was broke. Like the campagin that Henry V went on that led to Agincourt. He had 4000 archers cause they only cost him 6 pence a day. Where as the men-at-arms cost a shilling or two a day.