Oh, to be clear: Google will absolutely provide you a phone if you choose not to do this to your personal device.

... but if you're SRE oncall, you'll probably have that phone on you (or at least within hearing distance) at all times when you're on shift. I'd assumed the relevant issue was having a tracking device on your person your employer can access, not whether the employer was footing the bill for the tracking device they encourage you to have on your person.

Again anecdotally: most employees I know just set it up on their personal device. It's more convenient than carrying two devices around when one knows one'll be carrying a smartphone anyway.