It's a common misconception.
The Israelis didn't design or build the Desert Eagle as a combat handgun. As a matter of fact, they came rather late to the Desert Eagle story. Three fellows in Minneapolis designed the gun beginning in 1979, with a firing prototype running in 1981. They went to IMI in Israel for help in the final stages of design and manufacture, with the first production gun in .357 hitting the stores in 1983. The above .357 of mine dates to early 1984.
Were Elgin Gates still alive, he'd tell you what the big push was to make the gun. It was originally designed for target, silhouette shooting, and hunting.
Folks in IHMSA silhouette competitions were hand-grenading their magnum revolvers with hot loads, because they wanted the extra muzzle energy to reliably knock over the steel rams at the farthest bank of targets. Something had to be done, so IHMSA initiated the overhang rule to make the targets topple easier, but by that time, the Desert Eagle in .357 Magnum, .41 Magnum (Yes, and I want one!), and .44 Magnum handled the hotter ammo with nary a hiccup. IHMSA went dormant after Elgin died, but the Desert Eagle was here to stay, finding widespread use as a hunting and target shooting gun, too. During one IHMSA match, I pulled a shot low, into the dirt several yards in front of the steel critter. The round skipped off the hardpan and hit the silhouette, still knocking it over. I pressed on with the rest of the targets, but was suitably impressed.
Somewhere along the line folks got it into their heads that it was a preferred Israeli combat sidearm - and the myth continues to propogate to this day. Of course, Hollyweird didn't help matters much with their portrayal of the big gas autopistol. It's also the CounterStrike Kiddies version of the BFG-9000 as found in Doom.