Yes, it is the whole chart that represents the whole person.
But of course a whole person has feet, ears, a liver...all of which can be looked at separately. If the left foot has a thorn in it, it would be good to look at the foot.
The houses serve this function. They allow us to look at specific areas of the life when it is useful to do so.
As to the First House and Jung, call it the Persona. That is a very accurate description of one of the meanings of the First House. The House is more inclusive than just "persona", but in that role is the delight of Jungians everywhere.
The Fourth House can be seen as the "Collective Unconscious" while the "Personal Unconscious" is tucked neatly into the Twelfth House.
The problem you face is a blockage of understanding. Astrology is a universal language that, at least in theory, embraces "everything under the Sun" (that is, manifest reality). Each element of this reality can be placed in one of the houses. Quite often, a given element may fit into one of several houses, depending on its present state and also the personal perspective of the astrologer.
An example that comes to mind is "primary education", which can be given to the Fifth House. But this learning of collectively held knowledge, its acquisition by the native, eventually gives way to "higher education", which is exploratory in nature and deals with the unknown and the expansion of knowledge...a Ninth House matter.
Unlike the signs, which are cosmic in nature (they are divisions of the heavens based on the structure of the heavens), the houses are "mundane" or terrestrial. They are divisions of the heavens as centered on Earth...in other words, they represent the Heavens brought to Earth. They do not move, as the signs do, relative to Earth. Their symbolism is "immediately surrounding circumstances" or "earthly affairs".
All of us, at one time or another, face (our attention is primarily directed toward) all of the houses, sometimes with an emphasis on one house, sometimes on several. The affairs of one house, more often than not, have repercussions in another house, often several. A divorce (Seventh) may affect our Second House of personal liquid assets, our Fourth of home and family, our Tenth of career and public honor, and more. By using the houses effectively (through rulerships and aspects) we can see how these repercussions may act in the individual case.
My possessions (Second House, mostly) are an integral part of my being; I identfy with them, or they provide me with personal liberty to act as I choose (or deny that liberty in the case where such possessons -- liquid assets, primarily -- are lacking). This affects my entire being, but by partitioning these off from other aspects of being, analysis of the role of "money" in an individual's life, seen as separate or distinct from the role of "friends" in the Eleventh House, for example, is made possible.
In horary astrology (which answers specifc questions), one of the most important steps in interpretation of any chart is "assigning the proper house," which in some cases may depend on the judgment of the astrologer or the attitude of the querent toward the question. So, houses are flexible to some degree.
Again, it is a matter of understanding, and that is a matter left to the individual mind of the student. Astrology is fundamentally a "system of thought", and its efficacy resides in the mind of man. The houses are one of four primary sets of symbols that provide a structure, a framework, a discipline on which to hang our thought as we attempt to analyze character, destiny or immediate problems met in life.
House meanings (contents) have been tested in practice for nearly two thousand years. They are proven to work. I would not discard the traditional meanings lightly. You will find that different schools of astrology (compare Western tradition to Indian, for example) sometimes assign things to different houses. For example, in Vedic astrology the father is found in the Ninth House, while in the Western tradition he is allocated to the Fourth (or the Tenth by some astrologers). The personal death is an Eighth House matter in Western astrology, while it is given to the Second in Indian astrology. The apparent contradiction does not negate the validity or effectiveness of astrology, for as I mentioned, astrology is fundamentally a system of thought resident in the mind of man, and is not external to the mind. Astrological symbolism proceeds from celestial fact, and provided that the symbolism adheres to a logical derivation from those facts, it probably doesn't matter a whole lot what form the symbolism takes.
For example, the Fourth House cusp (the Nadir in quadrant house systems) is the "lowest" point in the sky. It lies "under the earth." Therefore, we derive the symbolism of "roots", "foundation", "the past"..... It is our "heritage", our family "name". It is all natural resources found on or under the earth. It is the collective or universal, racial unconscious. Being literally "under the earth" it is unseen, therefore our most private place, secret, hidden from view.
The First House is "self". The Seventh House opposes the First, and is therefore "not-self" as it relates to self, and is the house of marriage and partnerships, and of war and dispute. As you study the relationships of the houses one to another -- the crosses and the triads, the oppositions, etc -- you will see how they interlock and support each other, and in doing so portray the whole being in relationship to the environment, what it will meet in life on Earth.