No, absolutely NOT safe. In fact, climbing a pyramid can get you KILLED. Actually, climbing to the top isn't a problem - getting to the bottom is. A good friend of mine died from falling from the Great Pyramid of Giza in 1980 while studying abroad. In tragedy, I climbed it earlier that day with some other friends. Without a serious fear of heights, it is not very difficult for someone in reasonable condition to climb in 10–15 minutes.
But on the way down, you essentially have to jump down, stone by stone. Jump, jump, jump, hundreds of times. Remember, the pyramids were originally covered in polished limestone; they weren't designed as stairs. What's left are the ragged remains after looters removed the limestone layers to build the structures. The stones in the pyramids are uneven, ranging in size from a few feet to over 6 feet (see photo below).
Many of the footholds are smooth, slippery, and covered in sand dating back 4,000 years. The rocks can be slanted downward, too narrow, or cracked . There are few reliable handholds. With no fear, the climb feels fun and not life-threatening for those younger. While climbing, it never occurred to me that a small misstep could be fatal.
Imagine climbing the outside of a 45-story building without safety equipment. You really can't understand exactly HOW dangerous it is until you're up there and in serious danger. Imagine jumping off a ledge outside the window of a 35-story office building. I kept climbing to the top, but about three-quarters of the way up, I turned around and looked down, then immediately changed my mind. The 100-meter view straight down was dizzying.
My friend was quite athletic, but he slipped on the way down. This could have happened to anyone, as the terrain is steeper than it looks, so once you lose your footing, you won't stop falling until you reach the bottom.
[ Update : I just learned from some of my friends from the 1980s that climbing was already illegal at the time, but they bribed the security guards to keep them quiet. Interesting, no wonder no one bothered me when I climbed.]
Here's the view from the climb, near the top:
View from the bottom up: