The average Chromebook does a multitude of basic tasks, and almost everything it does is run through a variant of the Chrome web browser from Google. Given the basic instruction set and the lack of a need for compatibility with a wide variety of programs in most Chromebook use cases, a number of successful Chromebooks down the years have gone with ARM processors, choosing them for their power savings over x86 processors, among other reasons. In the mobile phone market, Qualcomm's Snapdragon processors dominate. You'll find them in just about every major handset in the US market, and a great many abroad. Some may notice that there has never been a Chromebook with a Snapdragon inside it. As it turns out, there probably never will be, and there's a good reason for that. Former Googlers Olof Johansson and Micah Catlin explain it quite nicely.
Custom ROM and kernel developers will tell you a couple of things about open-source drivers in the mobile world. They're what makes it possible to reverse-engineer a device's software and provide a good, working custom ROM, and Qualcomm is not 100% on board with them. Mainly in the graphical parts, but also in some core Linux kernel interaction areas, Qualcomm chooses to keep their processors closed-source, and not hand over their code. The reason that makes Chromebooks unable to use Snapdragon processors is actually pretty simple; Chrome OS is mostly open source, with a code repository showing off most major changes publicly. We can, however, pry a bit deeper into that.
When a Chrome OS device is coming down the pipeline, additional code has to be added to Chrome OS to support its hardware. This code, since it's not part of Google's closed-source, in-house code, will be open-sourced under the same license as the rest of the OS. That's actually how intrepid Chrome OS code sleuths often find out about new devices getting ready to ship. While Qualcomm could simply throw a prepackaged code blob at a manufacturer for use in one specific Chromebook, a big feature of Chrome OS devices is that they're kept up to date in a very close manner with upstream code. With Qualcomm's code being closed-source, developers couldn't keep it up to date. Qualcomm would have to hand-update code for each and every device on each and every release in order to keep a device up to date. This means that anybody buying a Snapdragon-based Chromebook would be left out in the cold for updates unless Qualcomm really wanted to work hand in hand with vendors to make each update, and updates happen pretty frequently with Chrome OS devices. Thus, until Qualcomm sees fit to open-source their core kernel drivers, at the very least, a Snapdragon Chromebook is not a very appealing option, and will probably just plain not happen.