I don't think a split off "Google Services" could survive. Google's fabric is designed to run Google's apps and vice versa. You can't just cram some other company's software into Google's core fabric and you can't just run AdSense on someone else's cloud. ETA: this is partially because of historical accretion and path dependence, but also because offering services at Google scale and reliability is a legitimately hard, abstraction-breaking problem; most fabrics aren't architected for the fault-tolerance and scaling that Google's fabric is (did you really isolate concerns? Are you sure your backing-store is eventually-consistent lock-free?), and most software isn't designed to run on a fault-tolerant, high-reliability fabric (what does your UI do if half the database is missing for ten minutes? Did you break your storage down into a NoSQL database with massive data denormalization because space is almost free, or are you using a relational database with heavy cross-lookup constraints that require high availability? Are your RPCs doctored with enough data to make for useful full-service traces, or do your microservices just spit JSON at each other?).
(Source: was there; I saw enough acquisitions go sideways to know how actually hard it is to reshape software from the outside world to fit Google's way of doing computing).