For a phone to opt in to the Android One program, in which the software is controlled completely by Google as you said*, it has to comply with a series of requirements. One of them is a closed and short list of hardware. The main cause of Fairphone is fairer electronics, which undeniably implies accurately choosing and cherry picking SoCs and components based on working conditions of manufacturing, and furthermore for the FP2, repairability, modularity and longest life cycle. In some cases, negotiating directly with vendors for specific extended security support or even full source code.
Fairphone needs a flexibility for fulfilling their promises and being what it is. Android One doesn’t offer the flexibility needed because of obvious reasons (they can batch-upgrade phones like Apple does with iphones because they have a limited list of hardware).
Furthermore, Android One’s promise of platform updates is already available for all phones as long as Treble is supported (mandatory for Oreo devices), as exposed by @Paule and @ben, and the possibility of other supported and alternative OSes like Fairphone Open/Lineage OS/Ubuntu Touch/Sailfish OS would be ditched, as already explained by @Stefan.
Sumarizing all this rationale, I’d clearly say NO to Fairphone surrendering their values and liberties to the Google monopoly and the Android One program for pretty little benefits.
*= that is very different to how current AOSP-based development + GMS is done and distributed with a “Google approval” (CTS)