I'll do the obligatory warning about lead in the Desert Eagle, even though I have no personal experiences using a bare lead bullet in said Eagle...
The gas port for the operation of the pistol is right at the point of obturation for the bullet.
My Eagle's first barrel had a very rough bore at this and other spots. I shot it first, as sometimes you just never know. The copper was cut from the bullet so severly it left a copper flare at four o'clock on the muzzle and a pretty patina of Orange around the piston. (Which was replaced in seven days by Magnum Research. Very cordial on the phone and great service.)
The point being that when a lead bullet is fired it is in the process of expanding as it passes the gas port. This shaves lead and deposits it in the tune. The next round melts it and packs it in the necessary u-turn, stopping the gas and fun.
It is said that an unwitting human may then fire many more round single fire, thoroughly filling the tube, rendering it a paper weight.
But, again, not personal experience. I just follow the directions, my life is simple.
That is only the way I have it reasoned out in my head, based on my barrel experience. Were it flame cutting and lead vapor a gas check would work, wouldn't it?
However, I have been wondering about coated bullets in the Eagle.
This barrel's gas port resides in a groove instead of a land. I wonder if it were polished by over a thousand Berry's plated and eighty overpriced factory rounds, if the coated bullets would work?
I like some of the brick wall meplats on some of those cast bullets...