(sorry for tl;dr post)
And it is about as useful as Android without the Gapps.... you can listen to some music, keep cool on a hot summer day, etc... but you really lose what the car was designed to do. Fact is that without the Google Apps, these phones lose a substantial amount of their functionality. And while there are some people who will load an AOSP-based custom ROM on their phones WITHOUT loading gapps, they are an extremely small (somewhat tinfoil hat wearing) minority. Fact is that the overwhelming majority of people run, and rely, on those Google apps and services.
But like JD said, Google's own version of Android is as close to 'pure' Android as you are going to get. They add functionality without forcing you to deal with a heavily modified UI and layout. Settings, Quick Settings, Notifications, UI look and feel... all that background stuff... they aren't screwing with that. The biggest 'look and feel' change they make is the Google Now Launcher that they throw on Nexus devices. But as far as launchers go, GNL is a really barebones launcher that hooks into Google Now (Google's killer app, IMHO).... but that is just a launcher that you can replace if you like.
Yes, Android is open source and OEMs are free to modify it to suit their own needs. But I think that Google is quite aggravated with how perverse things have gotten. Look at the Galaxy S5. Samsung has basically taken a Ferrari 458 and slapped on a few dozen extra gauges and screens and a 4000lbs trailer on the back. There are millions of smartphone users whose ONLY experience with Android is various iterations of Samsung's abomination. And I find that quite sad.
When people reviewed the Nexus 5... or even the Moto.... they will all, invariably, praise the OS and how much of a breath of fresh air the OS was. Why is it that the Moto X, with relatively underpowered hardware, could perform as well as it did? Motorola didn't sprinkle in some magic processing dust, they just chose not to slow the phone down. When they talk about OEM Android flavors, the best they can come up with is "Well, I guess if you have to pick one, Sense is not that bad". Glowing praise indeed.
So that seems to have emboldened Google to try to 'take Android back' a bit and both improve the experience and try to establish some kind of consistency. OEMs? They need to stop thinking they need to pee on the tree to mark their territory... they are trying too hard. Google is banking on the fact that, if really given the choice, people will gravitate to a 'cleaner' version. Now, this seems to have ruffled some feathers a bit. But to be honest, I embrace it with open arms. If there is one thing I've learned from owning Nexus devices (2 5's and a 7), it's that I'm on Google's bandwagon when it comes to what they do with Android.