Maps is doable, openstreetmaps is not bad or license from Here (or both). I'm not sure how many people need translate on a regular basis; I bet you could license that from someone though. Photos backup just takes money for storage, it's not particularly hard (you could instead work on making it easy to store with the end user's choice of provider, possibly with a revshare)
The real thing pulling to centralization is Google push, which requires play services, which requires playing by Google's rules.
If you don't have Google push on Android, you have to allow all the apps that want to get notifications from the server to keep open their own connections (which they may not have code for), which is going to kill battery life. The alternative is doing your own push services, but then you need to convince apps to support that, which generally requires apparent probable market share. Amazon managed to get some apps to do it for the Fire phone, but that didn't really go too well.
I actually think maps is the easiest to replace. We have bing maps, HERE, waze and multiple open source projects.
Waze is also owned by Google, but other than that I think it's a good point that there are a couple of other viable maps options. But still, you need something that actually works well, or you'll get to re-live the fiasco that was Apple Maps, so I don't think there are more than a couple viable options.
There are substitutes for Search, Gmail, Apps Suite and Chrome, but the rest of the basic services are not that easy to replace. Maps with turn-by-turn directions, Google Translate, Google Photos with unlimited backup are all essentials for mobile consumers nowadays.