You could also ask why the photon is necessary, if electromagnetism is a classical force based on Yang-Mills fields with gauge group U(1). Or also, why the gluons, the W, Z AND the Higgs boson are necessary, since non-abelian Yang-Mills fields are also meaningful as classical fields. In my opinion, the answer to this question, and why fields are to be quantized, must include two subtle issues:
- Quanta are not fundamental, but, as previous questions remark, are excitations from vacuum of certain FIELDS on space-time. What is relevant is the quantization of the action, that generally implies the quantization of energy and other magnitudes like angular momentum.
- Gravity has a different status with respect to other forces due to its universality, not due to it being a "pseudo-force". Gravity couples to everything, while other fields couple to certain properties of space-time like electric (magnetic) charge, flavor or color.
Moreover, the question of the need of the quantization of the gravitational field is evident when seeing the Einstein field equations for gravity: one side is the matter-energy having mass, energy, and quantum numbers, the other side is the geometry or metric of space-time. If identical, well, one should wonder if the metric itself has these features. String theory or loop quantum gravity show differently how the space-time itself could handle with quantum numbers. The problem with quantum gravity is not that we don't need gravitons. Indeed, Newton's gravity itself imply certain field theory in the form of Poisson equation that Einstein himself used as model to reproduce an analogy for building up his equations for gravity. The problem with quantum gravity and gravitons is in the heart of your question: if we model space-time like a metric and geometry, why do we need gravitons? We need gravitons because they must be there. Quantum theory is correct, even if some day is proved to be uncomplete or it must be modified to include gravity. Maxwell's equations are superseded by QED and the electroweakt theory at high energies, there new particles appear: the W, Z bosons and the Higgs (for consistency). Conceptually, maybe, the issue is understando how a set of gravitons could determine the geometry of the metric? No, the issue with gravitons is that General Relativity in a canonical quantum theory behaves badly. Calculations diverge. By the other hand, the space-time metric, the one in General Relativity, can not be the whole story...Just we know the Standard Model is not the whole story...The spacetime metrics in some concrete circumstances also diverge CLASSICALLY! Every theoretical physicist know that space-time singularities are a problem in most of the classical theories of gravity. You get singularities in black holes (hidden under event horizon, due to the cosmic censorship hypothesis), and you get singularities at the beginning of the time...In both cases, you have a very dense object in a very tiny space. Such extreme density conditions make us think that General Relativity and the description of space-time with a metric is only an approximation or a very good model excepting extreme cases (black holes, the Big Bang,...or similar). There, enter quantum gravity and gravitons. Graviton scattering must domine in such regime or produce some kind of extreme "matter"/object whose description with a metric is bad. Of course, some people work on the idea that black holes and space-time is some kind of "condensate" of gravitons or superfluid made of some preonic substance yet to discover (the nature of the microstates of black holes is only approached in some extreme cases with superstring theory).
1) A graviton is necessary due to universality description of all the forces as interchanging force carriers.
2) A graviton is necessary since we believe graviton excitations, maybe Wheeler's space-time foam in some form or alike, must dominate the description of very dense objects (microscopic black holes, the beginning of the time, and other similar examples as space-time singularities).
However, graviton scattering behaves badly in general relativity. Taking a conservative canonical quantum gravity approach provides divergent results. Only string theory and loop quantum gravity, and some minor third ways to quantum gravity, shed light on how to calculate these divergences.
String theory provides a unifying framework to handle with all the "fundamental forces" and matter field. However, after two revolutions, and no hints of extra dimensions in experiments and detectors (and a critical 4D value from gravitational wave observations to date), we have no evidence from strings or p-branes yet. Loop quantum gravity (a modification of the canonical quantum gravity approach) provides an example of the quantization of geometry using a different technique than that in string theory. Area and volume are quantized in LQG. What are gravitons then? Gravitons in string theory are certain kind of excitations of the fundamental string (or brane). This fact is also remarked in the emergence of a symmetrical tensor when calculating the excitations of the string from the "vacuum". Gravitons in LQG are more subtle, I imagine them like polymer-like excitations from the area and volume operators, derived from spin networks and other discrete structures of the theory (I am not expert on that field, so I am being imprecise quite likely...).
3) Gravitons, photons, Higgs bosons, gluons, are likely not fundamental...Why do we need them? Because quantum fields can be represented as entities whose excitations produce particles. It happens with fermions as well. There is only a single electron field in all the Universe. However, the excitations in that field are the electrons we observe, reverberation of the beginning of the time...Just like gold atoms are produced in supernovae, electrons (or quarks) in the Universe were produced in the farthest past, and what remains is a rest from the annihilation with vacuum billions of years ago.
Gravitons, like photons and other particles, were produced in the beginning of the time. We don't understand what happened there, when GRAVITON scattering was dominant since the temperature was so hot, and the density so high, that we can not neglect gravitational interactions, usually weak when present electromagnetic or nuclear forces, or negligible only when you are not in a place where you have dense matter in a tiny volume (microscopic AND heavy black holes). That is why we need to understand better gravitons. Before the discovery of gravitational waves, that by duality imply the existence of the gravitons, some people wondered if gravity should be quantized. I think that question is not (if ever it was) relevant now. Gravitational waves do exist and then, gravitons (in some form) may exist. But, this have nothing to do with the classical existence of gravity. Before the Quantum Mechanics, physicists discussed if light was a wave or a particle. Well, light is both! Why do we need PHOTONS? We need photons since without photons (quanta of light) we could not explain wavy the photoelectric effect or the black-body radiation. Indeed, you are all embedded in a cosmic microwave background of photons emitted by the Big Bang, with temperature about 2.73 K. We believe there are also a neutrino and a graviton background as well. So, we need gravitons as well to understand the Universe! We can not understand the beginning of the Universe without understanding gravitons and the quantum nature of gravity.