Why are gravitons needed at all? Okay, very much an amateur here, but I am curious why gravitons are deemed necessary.
As I understand things, the other forces need their force carriers because there is an interaction between particles. An excited electron shifts to a lower energy state, and at the same time emits a photon. Some time later that photon may interact with another bound electron in some other atom and depending on the situation either shifts that electron into a higher energy state or knocks it free from the atom entirely. And the strong and weak forces, while different, at least more or less behave like this.
However, if gravity is actually stress placed upon spacetime itself by matter and even energy this would seem to be completely different. In this view two masses would 'attract' because they each place sufficient stress on spacetime rather than because there is any interaction between the two. Something like the Cavendish torsion-balance experiment would just be showing us that stressed spacetime in ways that our senses are not well-equipped to demonstrate. Gravitational radiation (as from in-spiraling black holes) would then just be a different sort of stress on spacetime. The moving stress itself would be the carrier of the released energy.
So, again, why the graviton? What does it add?
 A: First, I think it's worth being careful with statements like "gravity is $X$", where $X$ is some mathematical description. (Like, "gravity is curved spacetime."). That is a good description of a theory (in particular, of general relativity), but it may turn out that our current best theoretical description (general relativity) is not the best one to describe Nature in all situations. Particularly when we are talking about quantum gravity, for which we have very few established theoretical or experimental facts, I think a safe attitude is to keep an open mind about what the final theory that describes gravity will look like.
Having said that, there is a regime where general relativity mathematically looks just like the kind of "ordinary" gauge theories that make up the standard model, but with a spin-2 particle mediating an interaction instead of a spin-1 particle. This is the regime where spacetime is approximately flat, and the departure of the metric from a flat spacetime is "small".
In this regime, one can set up a consistent approximation scheme known as the effective field theory of gravity that allows one to compute quantum gravity effects perturbatively in powers of $E/M_{\rm pl}$, where $E$ is the energy of the process and $M_{\rm pl}$ is the Planck mass. In some sense this approximation scheme is very "natural" -- we do not need to introduce any additional equations besides Einstein's equations, and we just apply the normal rules of quantum field theory and effective field theory that work for the Standard Model.
Within this approximation scheme, gravitons naturally appear as excitations in the gravitational field, in exactly the same way as photons appear as excitations in the electromagnetic field. It is not that gravitons "add anything" or that we "want" them; they are just an inevitable part of the formalism. In order for gravitons to not exist, there would need to be a reason why the effective field theory of gravity does not work, or in other words that we cannot apply our usual tools of quantization to Einstein's equations directly in a regime where we would expect to be able to do so theoretically.
With that said, there are two caveats to consider:

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*While theoretically, the effective field theory of gravity is well-motivated and natural, it has not made any new predictions that have been confirmed by experiment. In fact, the main prediction it makes is that quantum gravity corrections will be suppressed by powers of $E/M_{\rm Pl}$, which will be utterly negligible for current or planned experiments.

*Gravitons are a natural part of the formalism, but unlike photons they will interact extremely weakly with any kind of detector. In fact, Freeman Dyson wrote a paper exploring whether any conceivable detector could ever detect a graviton, and was not able to come up with a design where a graviton could be detected, even with wildly optimistic assumptions. For example, attempting to build a "LIGO-type" interferometer that was sensitive enough to detect a single graviton would inevitably lead to the detector collapsing into a black hole under its own gravity. https://publications.ias.edu/sites/default/files/poincare2012.pdf
