I think that it looks quite like an obelisk - the earliest obelisks were quite squat.
The burial place of Shepseskaf (last king of the fourth dynasty and successor to the builder of the smallest Giza pyramid) was not a pyramid although the Egyptians sometimes described it as a pyramid. Some people say it looks like a sarcophagus and others like a shrine.

The Bent is most assuredly a pyramid. It's "bent" shape was achieved when the original building of the pyramid started to settle, shift and crack. The builders thought that changing the angle of the slope could help correct the grave situation. It did help, but not enough. There are still large cracks and shoring up with timbers that the builders tried.
The fault was not the slope of the pyramid, however. When the original base was laid out, the builders did not clear the ground down to the bed-rock. The building was constructed on a layer of sand--and of course, this ultimately shifted and settled.
Even though the pyramid was completed, Snefru was not buried there. He had a third constructed, the so-called Red Pyramid, which is his best. His original place of burial is not known for sure.

It seems to me that it would have been impossibly high if it continued to a point at its original angle even if the foundations held.

Not "impossibly high". It would have been the highest structure made in the ancient world.
In fact, the GP was the tallest structue in the world until the Eiffel tower was built in the 19th century, and the Bent, if not bent, would have been (I think) about 20 feet taller.

I looked the bent pyramid up in a book (the Complete Pyramids). I do not know if it is my memory or an optical illusion but in real life the 1st stage seemed a lot steeper than it realy is

The original angle was almost 60 degrees. When it was changed, the angle became 55 degrees.

You might find this information about the Bent interesting to read:
http://www.touregypt.net/featurestories/snefrubentp.htm

Touregypt is usually very good in their accuracy. Unlike much of the on-line information...