I think this overemphasis of the "particle picture" is a source of misunderstanding. A photon has the least particle-like properties of any "elementary particle", because it's massless and has spin 1 and as such has no position observable in the usual sense. In relativistic QT it's anyway even less possible to localize "particles" than within non-relativostic QM. The reason is that if you want to confine a "particle" to a small region in space you need pretty strong fields to do so and due to this interaction rather than confining the particle more to the small region you create more particles. That's why a single-particle picture is problematic in relativistic QT, because of the possibility that in interactions particles are destroyed and new ones created. That's described most naturally by a quantum field theory, and that's why relativistic QT is described as a quantum field theory.
Another advantage is that a field description of interactions is a local description, i.e., there is no need for instantaneous actions at a distance to describe the interaction between particles. That's the great achievement by Faraday and Maxwell which lead to the discovery of classical electrodynamics, and in 1905 it became clear that it is indeed a relativistic field theory, which can quantized to get Quantum Electrodynamics. This description also solves the notorious problem of causality, i.e., it enables a description where by construction no causality violations occur, i.e., there are no causal connections between space-like separated events, i.e., any interaction can act over a distance with a speed less than or equal the speed of light.
Thus the mathematical description leading to successful relativistic quantum-theoretical theories all hints at a field picture, and indeed it's much more natural to think of a photon as a certain state of the electromagnetic field, a single-photon Fock state since this is the, admittedly pretty abstract, description where the socalled "wave-particle duality" (a contradiction in itself!) of the old quantum theory is resolved into a consistent description. Particularly it describes both, the wave and the particle aspects, in the behavior of a single photon in a consistent way: On the one hand you have the interference effects leading to a double-slit diffraction pattern when collecting many equally prepared photons on the screen and on the other hand that each single photon can make only a single spot on the screen, i.e., it can be absorbed as a whole or it's not detected at all.
The prize the founding fathers of QT had to pay was that they had to introduce the probabilistic meaning of the quantum state, i.e., that even when the photon's state is as completely determined as one can observables don't take determined values but when measured you get a random result with probabilities described by the quantum state. E.g., you can't say where an individual photon will hit the screen when sent through the double slit but only the probability distribution for where it will be measured, and this probability distribution is observable only on an ensemble of equally prepared photons.
