I am in charge of IT security for my company and in my experience users like you get put in a tough place. On one hand, you want the freedom to work however you like, but on the other hand the company has real requirements and limitations imposed on them that necessitate dictating how end users compute. I am also guessing that for every user like yourself who would gladly use a company provided device to keep their personal and work computing separate, there is a corresponding user who absolutely will not tolerate being forced to use an additional corporate machine and will complain until blue in the face about it. It's a lose-lose situation for IT.
There is also the matter of endpoint protection to consider. If I am allowing a personal device to connect to my environment, how do I know that device is secure? The only way to have any level of assurance to that fact is to install remote monitoring agents, inspect the configuration of the system, and restrict administrative permissions so the end-user (or an attacker who hijacks the end user's access) cannot mess with things in such a way as to compromise the already shaky ground the integrity of that system stands upon.
If I worked at your company, I would give two options: either use a corporate machine for work activities, or if using a personal machine for whatever reason then IT gets administrative control of the device. There is no third option. And before IT assumes administrative rights to manage the device, the end user is signing an acceptable use policy that they agree to any and all IT security controls placed upon the device. If that is unacceptable then the alternative is always to use the corporate device.
I am not sure if you're an FTE or a contractor or what your locale is, but IMO imposing that kind of control over a privately owned device without an agreement would be at best inappropriate, and potentially illegal. My response would have been "No, thank you." I do however sympathize that it is not always possible to take that stance.