Not really. Google sets strict boundaries for smartphone brands on what they can do software-wise. For instance, iirc, shipping the phone primarily with a non-Google alternative ROM means you won't get any play services on them, even if you want to have a secondary version with a standard Google ROM.
Google has essentially full control. Because they own security updates. Because banking apps already now often do not work without Google services. Etc. Etc.
It is a monopoly (regarding Android app developers), and is increasingly exploiting that to cash in.
Actually, the phone doesn't have play services if the vendor doesn't install play services. If the vendor installs play services then it has play services.