Where I work, everyone has their own virtual machine accessed via a zero client. Some of us have a physical CPU under our desk as well. I take my Pro to meetings and when I need to do something that can't be done natively on it, I'll remotely connect to my virtual machine or desktop and take it from there. The only sticking point has been the lack of mouse support for those remote sessions.My company is actually super iPad friendly--they have worked really hard to get all of our internally developed stuff on iOS, and there are iOS versions of all our other software available on iPad as well. They encourage us to use our smartphones and tablets and even let us use our Office 365 licenses on our iPads if we want to.
But I do have the same issue with VPN and I also have worries that if I show up to meetings with just my iPad Pro, I'll be asked to do something it can't do. The chances of that happening are slim, but it's still possible.
I do think though that some day my company is going to get to the point where we really can work 100% from our iPads. For now though, I will have to lug along that Windows 7 Dell.
Love being able to tote my iPP rather than a notebook to meetings.