And I can install a 'Skype stub' application that doesn't do a thing unless you start it as well.

It's still crapware, unwanted and useless. If I want anything but the Play Store (honestly.. I shudder, whenever I have to write/say that name. How can you take that name serious, ever?) itself, I can install it. Preinstalling applications is a Bad Idea™ most of the time, clutter if you're feeling nice, abusing the market position otherwise.

Why would I need Chrome on my mobile? Why is it impossible to remove it?

Play Services is running all the time by default. It's default configuration is to run location services, which is highly battery intensive, to report your location to Google on a regular basis... a huge privacy issue. The Play Store auto-updates all these Google apps by default, which can use a lot of data. Play Services can and does update itself even with auto-updates disabled.

It's very hard to justify Google Play Services as anything other than malware, because it has all of the primary functions and behaviors of a virus.