I had always thought compound bows were far superior to longbows?

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I've heard the same thing about the gear manufactured in the 20th century - but I hear somewhat different stories about the bows manufactured in their time. My childhood experience of trying to manufacture a single-piece longbow does not concur with the claims of modern manufacturers.
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Maybe that is because, as children often do, I did not follow the instructions and, consequently, I did something different. It was a bit rough. I'd thrown it together from a one inch diameter hardwood branch (redgum, I think) and it was somewhat frustrating because I could not reproduce the building power curve that would have given me a yardstick in terms of my own attempts to use the bow. In my case, this inefficient building power curve would have allowed successively more draw as I built up my strength - but it didn't work that way. The force required to hold six inches or twelve inches of extra draw on my piece of handiwork was indistinguishable without measuring equipment - and well beyond my ability to draw in such a way as to allow me to aim at a target. It might have been very "efficient" for someone else but I liked having my arms in their sockets - so I let it go.
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The moral of the story is that materials, design and technique can make a tremendous difference - especially with the things that seem simple. So maybe the historical stories are just fables, but in the light of my own experience they seem plausible - at least when it comes to the longbow.

Crossbows were removed because they had a nasty habit or never hitting anyone in the knee.