Does anyone know the reason why, in SpaceX's newly-announced ITS launch vehicle, only the inner cluster gimbals, and not the whole engine system?
The main issue is one of size. Each engine bell requires space and with 42 that is a lot of space.
In order to gimbal there needs to be room for the bell to actually move, which means you need to space the engines further apart.
But just allowing the inner ring to gimbal they are the only ones who need the extra space, which you can see in the image cited in the question. Since this suffices for control, why do more? Also the hardware to gimbal is more mass, more cost, so if possible to minimize, why wouldn't you?
Optimally packing the engines, the outer rings would contain 12 and 18 respectively, for a total count of 37 engines.
Requiring space around the inner 7 to gimbal them, means adding more engines in the outer rings, allowing the designers to bring the total count up to 42.
Besides the points raised, that a cluster of engines would need space to gimbal, and the fact that the outer engines can throttle which can also “turn” your rocket, an engine with the apparatus is slightly heavier and signiicantly more complex than a fixed one.
Another thing I have the impression might be true is that “gimballed” engine closer to the sides would create a less sound structure.
Here's an alternate angle to contemplate (no pun intended).
Vectoring engines carries some risk factors the engineers must consider, as with most any sub-system comprising the overall vehicle.
In a failure scenario, a hard over gimbal actuator presents a flight emergency that of course they would want to be able to compensate for.
Perhaps the central cluster provides ample response and adequate control gain without needing to have the added complexity of all engines vectoring. It's not hard to imagine the cost increases associated with implementing the added gimbal mechanics, and the proportional increases in flight safety risks.
Another aspect which I'm admittedly and obviously not versed in regarding the actual flight control and stabilization techniques employed on this vehicle, would be the possibility (if it isn't like this, then I've maybe spawned some unique approach) that having adequate vector influence on the flight profile with the center vectoring only, the outer (ring) of non moving engines can be throttled differentially for some degree of angular deflection of vehicle's flight path— since those engines are ringing the outer portion of rocket cross-section, and would inherently have some appreciable effect if they were throttled in coordinated manner to induce deflection of vehicle trajectory. In that spirit, flight control might be achievable with no gimbals at all, had there not been the intended capability of a powered descent and landing.
Anyway, there are multiple ways to approach solutions like this, and unless you are experienced in developing vehicles like this and working through the process that results in deciding the methods that solidify the final design (i.e. spending a lot of money, winning some gambles and scraping by risk factors without accident) we just have no real idea why things end up configured as they do… although it's safe to say that we are not required to know squat about it for it to work in the capacity intended.