Why didn't Google just take a Linux distribution ... and create a desktop environment for touchscreens?
Because they didn't want to create a desktop environment for touchscreens: they wanted to create a new OS for smartphones. Smartphones (and earlier, PDAs) based on not only the Linux kernel but the GNU userspace, with the same programming environment as desktop Linux, existed for years before Android did, but they were a huge commercial failure.
The chief advantage of using a GNU/Linux distribution is the idea that you can simply recompile all the same applications for your new hardware, rather than having to write a new application. But this has never worked out in practice. A user interface designed to work with a keyboard and mouse on a big PC display simply doesn't work on a phone touchscreen. The ways that programs interact with each other on a PC with almost unlimited storage and no need to conserve power simply doesn't work with the limited energy and storage requirements of a phone. The pixel-layout, fixed-dpi ways of designing graphics and user interfaces for PC displays have already been outgrown for PCs, and phones need something better. In addition, smartphones introduce new features - ubiquitous location availability, cell modems and telephony, and Bluetooth - which PCs have never offered applications a standard way to access.
The Android team set out to offer a programming interface (the Android framework) to let app authors access all the needed functionality, in a way which wasn't previously available. They set out to isolate apps from each other to protect the integrity and the battery of the device in a way that wasn't possible in any existing Linux distribution. They set out to create a new graphics subsystem to avoid falling into the Linux community's dependence on X Windows. They set out to create a commercial success, which had never previously been achieved with Linux-based handhelds.
They achieved all those goals, by doing exactly the thing you complain about. Android is much bigger than just some Linux drivers, and many kernel drivers for Android devices do eventually make it back to mainstream Linux.