There was a great website that I read a year or two ago about the history of the P-47, including opinions on why it was relegated to mostly attack roles towards the end of the war while the P-51s "got" to do the bomber escorts. Unfortunately I just did a few google searches and I wasn't able to find it again.
Most historical accounts will claim that the P-51 assumed the role of escorting bombers from the P-47 because it was the only aircraft able to stay with the bombers the entire time. But from what I recall, the web site I was looking for claimed that the Jug's fuel capacity was upgraded to allow it to escort just as far as the P-51s, around the same time that the long range P-51s arrived in Europe. So why did the US send their pilots out in the lighter armed and armored P-51s? The conclusion I came to, if the previously-mentioned was true, was cost. The P-47 was more expensive, both in cost per aircraft and cost in fuel consumed per mile, than the P-51. The lives of the pilots were either cheaper in comparison, or they weren't factored in.
As an aside, even if its true that the US didn't protect its WW2 pilots as much as it could by sending them out in a perfectly capable P-47 instead of the P-51, I would hesitate greatly before calling it a "mistake"... we were trying to win a war, and there was no guarantee that the war would be won when it was, or that the money and fuel saved wouldn't be important in the end.