Well, it hasn't happened yet. That said, why would you cancel your cable Internet for this? Yes, cellular Internet will be useful for your Chromebook when you're away from home, but in the same way it is today - a useful supplementary service that fills in the gaps, not as your primary system.
As for how you'd connect to a server at home, there are two options: VPN, or IPv6. The latter tends to get forgotten, but I connect to machines at home directly via IPv6 from my (T-Mobile) cellular connection without any problems. This sounds horrifying in terms of security, but if you imagine the development server being as locked down as a Chromebook or iDevice, without the back doors associated with too many modern IoT devices, it should be fine.
I'm more bothered about having to develop using a web interface, especially in an era in which leaving Firefox open for a day with 20 or so tabs open seems to result in it eating 4+Gb of memory, not the connectivity part. The connectivity part is actually the nice part.