I've got a couple of thoughts on this -- it's one of my pet peeves, as well[0]. The first point is, and I get that this doesn't apply evenly depending on the kind of job that you have, but if you dislike a company policy ... find a new company. Particularly in software engineering, there's just not a lot of excuses for hanging around at a place that you're unhappy at. This isn't saying "don't like it, tough!" ... I find most people stick around at a job they hate out of fear or other false reasons ... it's "don't like it? Find a place that values you and shares your values". That said:

- I'll toss out a $10 bet that the same "don't ignore me by putting your nose in your phone during a meeting I'm running" applies to "don't ignore me when you're home, enjoying dinner with your family, and I send you a text/e-mail". A policy that forbids phone use while in the office, if matched with a policy that forbids responding/checking e-mail while at out of the office[1]/on non-work time, is a lot more palatable. My big rule -- and the one thing that has been the deciding factor of whether or not I would take a job or whether or not I would quit working where I was at is the answer to the question "Do they give me the tools and the freedom to do my job in a way that is sufficiently efficient and does not hinder me?" Generally speaking, companies with a lot of these kinds of "edicts" like "phones in meetings are prohibited" don't score highly in answering that question.

- Responding to people being distracted by their phones in meetings with "Bad the Phones" is text-book example of treating the symptom of the problem rather than identifying the problem. Speaking from personal experience and from anecdotes from coworkers over the years, the problem is the meeting itself. I'm not an advocate of tossing chairs out of the meeting rooms, banning meetings[3] all together nor am I generally of the opinion that most meetings are bad. The problem is that most of the individuals invited to a meeting are not needed, they know they're not needed, and they've got other things that they are needed for. In a lot of cases, these are the guys who are brought in because they're an SME on some corner of a project and their input will be needed for 5 of the allocated 55 minutes[4]. Get the answers you need from minor contributors through Slack (heck, you can even schedule them as a Slack participant so that they know to be near their PC in case a question pops up) or e-mail and stop inviting them to spend an hour at what amounts to "a different desk". It sounds like the company in question came to the right conclusion in the end -- stop going to meetings you don't need to be a part of.

- Somewhat unrelated, but I rolled my eyes a little at "I firmly believe that multitasking is a myth". While I'd agree that there are far more people who believe that they are "super-taskers" and are not, I have met two super-taskers in my short time on this earth and several competent multi-taskers. One is my wife, who could literally repeat back to me word for word the last 6 sentences I spoke with more accuracy than I could, all while continuing to follow the plot-line of a book she's reading and the other is a former boss of mine who I've never seen drive his car without holding a conversation via text and as many times as I had driven with him I had never felt unsafe. I'm not terribly surprised that the quotation was from a man (not meant to denigrate the individual) -- I've read that multi-tasking traits are less prevalent in men and, incidentally, I have yet to meet any male who can even slightly multi-task effectively except for my former boss (who wasn't just an exception to the rule, but a glaringly large exception). However, of the women in my life and in my past, all of them surpassed my multi-tasking abilities and easily half of them, I'd estimate, were quite good at it.

All of that said, there is a form of etiquette that I think is failing to be observed by a lot of us. Part of that needs to be established with direct communication. At the place that I work, when we have "all staff" meetings (which are the ones you really want to be dorking around on your phone), the owner asks us to give him and the others who are going to speak the time, without phones. No need to send out a passive-aggressive e-mail, just simply stated "Please pay attention, there's important stuff here" and he follows it up with "Thanks, everyone, for keeping your phones out of your hands" when it's over (and the rule is observed where I'm at). When I know I'm "the guy who they need for 5m in a 55m meeting", I say -- before or right at the start of the meeting -- "I'm a little back-logged and since you only need me for that part, I'm going to sit quietly here and get some other things done -- if I'm called on and I don't look up, feel free to throw something at me." I try to make sure the organizer knows in advance when I have to be distracted so that they don't think I just don't care and would rather catch up on Facebook (which I'm not a member of) or Reddit (which I rarely visit even on my time)[5].

[0] It wasn't always, but I think after getting one of my children a phone and noticing how he tended to be nose down most of the time, I notice it more.

[1] Something tells me they're not big on remote work. :)

[2] For those where work culture is different -- this is unusual enough of an act that when people who hadn't worked with me directly saw me do this, I'd be asked if I wanted the meeting start pushed back so I can run back to my desk to get my laptop.

[3] For the same reasons; stop treating symptoms.

[4] I'm frequently that guy. I have a lot of hobby interests that I follow closely that few others in my office have expertise in, so while I might have nothing to do with the work being done for a project, I may know something on the security side of things that makes my presence in a meeting a huge time saver for the organizer and -- provided I can sit in the room with my laptop and quietly code away until that nugget of usefulness pops up -- it's not a huge time-suck for me.

[5] Where there are gaps of understanding, people jump to the worst possible conclusion -- "he's probably screwing around instead of actually working because this meeting is really important" (just not to what he actually needs to get done).