"Hey I see you're on Stack Overflow a lot, are you having trouble with the work we've given you?"
Why do we think that nontechnical managers would be good judges of what productive behavior looks like? Everyone has their own style.
For software developers, designers and many other creative workers, work and life are intertwined. They can't, and often don't want to separate one from the other.
People often might fix urgent problems at night, or work extra hours on a weekend from home. But in exchange people want to be able to use company computer to check personal email, read the news, etc, and they don't want that email be available to their boss. That's a creative professional bargain. If employer doesn't accept later he won't get the former. And the value of the former is much higher than the later.
Yes, there're people who slack off, and they should be disciplined and fired if it doesn't help. But, if only people who you can hire are such slackers, may be there's something wrong with your hiring.
Any business worth anything has data to protect and insider threats are what frighten them the most.
Use your own device. On the Guest / untrusted network. With a VPN. Should you find yourself somewhere that doesn't let you do those things, and it's not a job involving a security clearance... then it's definitely time to shop for a new gig.
That doesn't mean those companies don't allow personal use but it has to be from devices on another network. Nowadays with most communication happening on mobile devices that's not much of an issue.
I though about staffing agencies creating digital sweatshops without any business justification for it.