There are quite a number of theories as to why an all seeing eye above a pyramid, appears on the dollar bill.

Clearly there are masonic connections with the originators of the United States of America and the original intention. There may have been as many as twenty one signaturees of the American Constitution who were Freemasons.
They largely reflected anti monarchist views and promoted European Enlightenment ideals of liberty and self governance. God was not encapsulated in a ‘religion’ but seen as an entity who largely left humanity to it’s own devices, whilst keeping a benign watch on things.
Also, the ‘eye’ on the dollar bill is clearly disembodied; without the arms and legs. This ideal of the Creator is more akin the gnostic view, than the Christian.
The symbol shows rays coming from the eye in all directions. This is important. Firstly the rays are coming from the eye, not into it. It is therefore akin to the sun and akin to the Ancient Egyptian deity Ra.
Whilst the human eye is perfectly adapted to receive and focus electromagnetic energy in the wavelength of light, modern science does not support the idea that eyes emit light. Yet in Ancient Greece, Plato and Socrates believed the eye was an organ that emitted a ‘fire’ to produce a ‘visual touch’ sensation. This reversal of what is today ‘the norm’ is not as nonsensical as it may seem. In ancient times the physical world was seen more as a system of energies, rather than the solid physical forms of today. Given that perception then it is quite possible that a human can feel with the eyes by emitting energy. We have all probably had the experience of someone watching us from behind or from a distance whom we cannot physically see.
The other symbol is the truncated pyramid above which the eye floats. The pyramid has thirteen courses and this number is repeated in other symbols present. It’s significance to the designers was clearly important and probably has several interpretations. Personally I would view it as a unification of the numbers one and three, one being the Godhead and three the Holy Trinity – in Christian symbolism which the Freemasons were most likely to use. At another level one interpretation I find interesting is by Swaller de Lubicz who said that thirteen is ‘the manifestation of the good or bad generating power’.
Swaller de Lubicz is a renowned investigator of the sacred sites of Ancient Egypt whose theories were unorthodox but very interesting. His book ‘The Temple in Man‘ is recommended.
In the Old Testament of the Bible and Torah, God is just such an energy that passes judgement and destroys that which it does not approve. Although this image of the Creator is at odds with the New Testament, for the Jews and many other societies, God is not just ‘Mr. Nice Guy’.
In science, the physical universe is in a constant process of decay known as ‘entropy’ and creation; with entropy ultimately being the winner. Even our own bodies reflect this state, and one day our bodies will expire, despite constant renewal processes.
So the eye at the top of the pyramid is more likely, in my view, to be an ‘Old Testament’ eye. Whilst man has freewill to make mistakes and good judgements, so does the Creator. Divine intervention does not, in theory, take place however in a contradictory way is does. God permit cities to be destroyed as does man.
The all seeing eye of God is not just protection, as worn by many as a symbol in the Middle East and known as the ‘evil eye’ or more accurately – protection from evil.
So, why a pyramid and why one without a point? Most pyramids are pure representations of the geometric pyramid form. To do otherwise is rare but there is one and it is well known. It is the so called Pyramid of Cheops on the Gaza Plateau in Egypt. This was one of the first to be built and many of the latter pyramids were pale imitations. There has never been a ‘pyramidion‘ stone and it was constructed to have a flat platform at the summit.

In my personal researches, I have come to the notion that pyramids were constructed to accumulate electromagnetic energy (amongst other reasons). This was done using rock which conducts ions and between anodes and cathodes. In the base of the pyramid are underground water courses associated with the river Nile. These bring in positive ions to the pyramid to be draw upwards through the centre. They were never intended to be emitted from the point of the pyramid as most others do, because other uses of the energies were being made in the chambers.
Suffice to say that I believe most pyramids were constructed to emit a steady stream of electromagnetic energy, from a height and in all directions, to other pyramids. This was a world wide network as evidenced by the presence of ancient pyramids on all the continents, including Antarctica!
A Pyramid and Tesla Tower with similar construction

The concept of ‘mobile phone’ masts as a network of transmitters and receivers of information encoded microwaves, is something most a familiar with in the modern world. It should not be so extraordinary to imagine such a network existed in the past using more primitive materials but with sophisticated, intuitive software.
The pyramids were transmitters and receivers between computers. If you wonder how computers existed so long ago, I am of course referring to the human brain, a computer so multi complex that it will be several decades, perhaps never, when it is replicated by scientists.
A form of ‘telepathy’ is plausibly existent between people such as twins or even husbands and wives, who finish each other’s sentences.
The ‘all seeing eye’ or ‘all knowing eye’ is therefore quite plausibly something contained not only in the mind of God but also His construction, humans.
The Ancient Egyptians denoted the Eye of Horus as in the diagram below. There is a convincing connection between this stylised image of the eye and the cross section of the human brain. This includes the pineal gland where our ‘extrasensory perception’ originates and is known as the ‘third eye’ – another illusion to the number three.

The ‘eye’ is also at a poetic level the ‘I’ or feeling of individual identity within the multiverse symbolised by the number 3 or the Trinity. I and 3 is of course code for, 13. The American Constitution protects the political and human rights of the individual and was fundamental to the creation of a free state which the USA has enjoyed for centuries, (at least in it’s imagination, when such issues as slavery are concerned.)
You can see, therefore that the information contained as they say in ‘plain sight’ on such a lowly item as a bank note is the perfect place to maintain a profound cognisance intended by the ‘Founding Fathers’, never to be forgotten.