Imagine, you are connected with remote teammates via live video that is blurred by default. They can see you but can't see what exactly you are doing.
It takes one click to unblur. Unblur takes a few (from 3 to 9) seconds, for you to prepare. You get a notification that a colleague is about to unblur you.
Video is mutual - your video is seen only by those who have their video turned on.
You can overhear conversations and talk to your remote teammates spontaneously: clarify requirements, solve problems, share ideas, etc. on the fly.
Would it be comfortable for you to work remotely via such a blurred live video connection?
P.S. Specifically, I am talking about a live video connection provided by this software: http://videoworklink.com/
I have first-hand experience with having a corporate job where they installed screen sharing software and chatted up how great it would be for someone to be able to see exactly what you meant without having to come to your desk to answer your questions. I never once saw or heard if it actually being used that way, but my boss absolutely used it to spy on people and crab at them about various things, some of which I felt shouldn't have been an issue.
General rule of thumb: If you don't want people to do X, simply don't make it possible. That's better than making it possible and asking them nicely to pretty please be decent people and not do assholish stuff, thank you kindly.
AKA "Lead them but into temptation." Humans need zero help finding temptation and we really aren't half as nice as we like to imagine we are.
If they want to talk to me they can ping me on IRC (yes we don't use the newer stuff) or schedule a phone meeting. Video calls are only for very specific reasons.
Is the company in any way owning the server or proxying the video or a man in the middle in the communication between you and your peer? My company would absolutely do that, or consider that I can't talk about confidential information through this channel, rendering it useless. And if they do the man-in-the-middle approach, then I would be concerned over privacy of having the monitor me 24h.
But taking away that choice changes video.... instead of it being a friendly gesture of openness to the team, it is now a constant threat of interruption.