Fields aren't observable. If I sprinkle some magnetic filings around a magnetic field, I will see the filings move, and even conform to the force lines of the field. But, at the end of the day, what I am seeing is the behavior of the particles, not the field. If all that exists are fields, then reality wouldn't be observable, which clearly contradicts with what we observe.

Of course, you say that there "observable points" added to the field, but I don't see how this is different form just saying that there are particles in the field, since that's basically all a particle is, an observable point. Quite literally. Particles are understood as dimensionless points which are defined in terms of their observables.