It is that simple, though. Your management structure needs a better on-call strategy. Or needs to both compensate you for, and indemnify you for the use of, your personal gear.
I don't work there anymore, but I'm genuinely curious why you think that's simple. In theory, absolutely. In practice, though? Trust me - I tried to get a better on-call strategy. You're making a lot of assumptions there without knowing much about the company, their management structure, etc etc etc.
Why is it simple? Because you should never, ever need to use personal equipment or other resources for work use. If you're on-call, then the company should be providing the equipment needed to do those on-call duties, and pay for phone and internet charges accrued. If you're needing to use your personal stuff, then there's a problem, and the first thing to do would be to communicate this to your boss, and get the necessary equipment provisioned, be it a laptop to take back, or something else. Implicit reliance on your kit isn't even in the company's interest--what if it broke down, infected a customer with a virus or whatever. They and/or you might bear some liability for inability to provide service or to provide a bad service.