Or people are overlapping discussions without coming to fruition.

Or the current part of the meeting is well known by the person and they are bored.

There are a myriad of reasons why someone check their phones and laptops at meetings. I don't like it, I don't bring my laptop if not strictly needed (I'm presenting something or need to support the presenter), I don't pick my phone up at any time because I feel that is disrespectful.

With that said, I'm dying of boredom in some meetings where the meeting-holder does not have a clue on how to proceed with one, I constantly have to stop people on the third or fourth level deep of an unrelated discussion.

I agree on you having a rule for "no phones, no laptops" but then you have the burden on carrying those meetings optimally, if not you've failed and have no right on asking others to behave if you haven't provided a good environment for that.

Also: I don't like these kind of extreme measures on petty issues, meeting distractions is a solvable problem without the need to shame people, I'd definitely be on the wrong job if that is your stance.