For example we needed to program an Arduino-type board, but that's not possible with our work laptops (no admin rights, USB ports disabled, etc); we never found a solution other than a personal laptop. Or a colleague needed to run a supplier's simulation tool that needed admin rights, and couldn't get an exception fast enough. Or you need to run a Linux tool.
This is not very persuasive. What you really have there is two work laptops.
My personal laptop comes everywhere with me. Doesn't yours?
Also, corporate has given itself the right to search any and all devices on me while at work, so that's double incentive to leave the home laptop at home.
I've had to check an account while at work to deal with my kid attempting to pay college tuition with one of my credit cards. Also looked up records so he could call the DMV to rectify something. Yeah, sometimes they're things that can wait a day, but a break from bug hunting can be nice.