You can indeed. And I have to say, with the Model 2's performance that's no longer a stretch.
Some of us run more than just BrewPi on our wee machines (see
Raspberry Pints to run a metered tap list for kegerator or keezer) which can mean a directly connected monitor is desirable (or even necessary). Keyboard/mouse can be a mini-wireless thing (that's what I use). Network connectivity can be via wire or wireless (I've used both but have my keezer wired now).
Also, the link between the Arduino and the host (RPi or otherwise) is usually over a USB connection. This whole Bluetooth link was something I came up with because I have three coolers that want to be managed by one RPi, but they're too far apart for USB (by a lot). Bluetooth fits the need perfectly, I just had to figure out how to get it to work
fwiw, some folks are actually using laptops either running a Linux distro native or running Debian in a VM under Windows. So you don't necessarily need a RaspberryPi for BrewPi...
Cheers!