The root (huehuehue) problem is that you have a job title/description (sysadmin) but are not imbued with the power that goes along with it.

is there a concise term for this kind of situation

This is called dysfunctional, and in my personal moral system you are a victim of injustice. You seem to take it lightly, but there are enough who would be stressed out so much under those circumstances they risk mental harm. I'm not kidding. If you have a cow orker, you must speak up and change the policies.

There is no good technical reason why you should not be able to add a computer to your organisation that's managed according to principles that are normal for this decade. All the time you frittered away in work-arounds and being blocked from getting things done is already orders of magnitude more expensive than the potential harm that comes with just purchasing a computer and setting it up apart from the legacy systems. There's your business case. https://workplace.stackexchange.com/ can help further.