I am an owner of a company and I would never request or demand that any of my guys work live. Do they do live work, well technically they do because every time they jam a breaker in a panel or troubleshoot a circuit they often “work live”; but sometimes it is necessary to test a circuit for proper functioning of control devices, or similar activities.
The real question is what are the circumstances that you are working live? In residential, except for testing a circuit, I cannot fathom a reason to have anything live. In commercial again, I cannot see a requirement except you may have to install a cable or branch circuit conductors in a live panel / conduit so you don’t shut down the store, etc. Industrial is a bit different, where when you are installing and removing MCC buckets, changing control devices, etc you may be working live, but there generally is a host of “protocols” and equipment requirements to be met before that can happen.
Do I work live, yes I do on occasion. While I admit it may not be a good example to set for my crew, it is a choice that I make based on a number of risk factors (and almost 30 years in the field) and none of them are related to saving time or money. Generally it is related to diagnosing a situation with a faulty control device, but I have also been known to change a breaker, switch or receptacle too.
Do not let your boss push you into something that is not required and could be dangerous; there is basically no reason for it.
Based on your questions, I suspect you are pretty new in the trade; there are tons of avenues for you to explore but if you end up killing yourself because you are being pushed into something that is not required (and it goes wrong), you will never get a chance to see all the fine things the trade can offer.
Cheers
John