Our diaries and emails aren't open-access, unless you make it so, though HR could get access if required for some investigation.
I work for a big multinational. My department is spread across 6 countries. Apart from when we have to do physical datacentre work, location isn't that important, because have the team aren't even in the same country. It makes no odds to me whether they're in their local office or home, as long as we're all accessible by instant messenger, phone and email most of the day. We also use video-conferencing, so we know what each other looks like, and on the rare occasions people visit other offices, local people do tend to make an effort to physically be there, because meeting people face-to-face once in a while does make a difference.
I do go into the office most days, because I live alone - some years back, I wrote my car off, and ended up having to WFH for 3 weeks, and I felt very isolated, despite the fact that I can be in the office and not actually talk to the people sitting next to me if I'm really involved in certain types of work. Somehow, though, there is a difference. However, it's good to have the flexibility, so if the car's in for its MOT, I can work from home, things like that. I worked from home for about a month after my mother dies - actually I was working from my parents' house while we cleared it. It meant I could do things there in the evenings, and not have a 2hr journey there.
We have people on home working contracts, and flexible contracts so they can always be home for the afternoon school run or whatever. Most of us are pretty flexible - we have some people who come in early (works well with AsiaPac), others who come in late (works well with the Americas.) For me, if I have to be in for a 9am meeting, I need to leave home about an hour before; if I can wait to be in by 10am, the journey's about 25 minutes - HR have previously sent out notices encouraging staggered work times, as it is easier for traffic. Also, we have to cover 24/7 on-call with a rota, and sometimes out of hours work, and flexibility needs to go both ways.
A lot depends on the department. Some have to be physically on site (reception, security.) Some have issues around data security which means they are in a restricted office space. But a lot of us can work anywhere there is a decent internet connection, and some home workers are based a few hours from the nearest office. Some managers aren't as flexible as others, and some people do take the piss. I know my manager is more likely to let me WFH than some of my colleagues (or at least past colleagues - I suspect their productivity may have had a part to play in them not being current colleagues.)
Most of our trainees are currently in a different country. Screen sharing tends to get round most issues there, they can show what they're looking at, I can demonstrate what they should be doing. This might not work for all types of work, though. (I'm in IT.)
I believe those on a homeworking contract are meant to have a workplace assessment to make sure you're not going to sustain long term physical problems by unergonomic desks and so on, so working on the sofa wouldn't be accepted. I have worked from the sofa and bed when on-call... (I have also learned how to stop the camera on my laptop from automatically starting, to save any colleagues from me being bleary-eyed and not fully dressed on a 3am call...)
Flexibility can work really well, but it does need a shift in mindset - and technology can really help these days. I still like to meet colleagues face-to-face once in a while if possible - but that's once a year or less for most of my European colleagues, not every day. I haven't met most of my US or Australian or Indian colleagues at all, but if any are going to be visiting, I would make a real effort to meet up.