It works well in those cases. But actual ice melt happens over time. Given enough time and diversion to a warm climate such as northwest Egypt, the impact of that water diversion is reduced by a factor of more than a hundredfold.
The water, of course, does not disappear. It evaporates, it is stored in the clouds as water vapor, it soaks into the ground or it is stored in other forms. Throw in water consumed by cropland, forests or other uses, then you begin to see how the model indicated is not only logical, but likely.
Of course, it depends on which climate modeling data you use. If you use the catastrophic chicken little models of the global warming fanatics, we're probably already too late. If you use the more realistic data on global warming trends over time, then you don't even need a full Qattara Depression to accommodate current modest warming trends.
Only one thing is for certain: If some international consortium of companies announced that they were going to begin construction of a Mediterranean Sea diversion pipeline to fill in the Qattara Depression to assist Egypt in agricultural and hydroelectric development and, at the same time, prepare for global warming, you would get a huge outcry in opposition from the same global warming fanatic crowd predicting catastrophic consequences from the sudden lowering of the earth's ocean levels, the destruction of the habitat of some sub species of sand flea found only in that area of the world or whatever other claptrap they could conjure up to obstruct the project.
But wouldn't it be fun to try?
All your other suggestions are fine, we can use more energy, more arable land, more cooling evaporation (in case global warming is real), etc. The only problem is suggesting that this flooding will have any impact on sea levels WRT Greenland's ice. I prefer to point to the fact that the melt from Greenland is trivial and there's no reason to believe it will rise unless one is to believe certain climate models which are not driven by physics and cannot be verified.