The reason you do it in the meeting is that for more senior people, you have to block them off time to think about the document. Asking people to schedule another block of time to give feedback on YOUR problem is rude. As you get more senior you end up in way more meetings. It's hard for more junior people or ICs to understand in a lot of cases. If timing is hard, have them schedule you in a different slot.
You can tell in say google docs where everyone is reading wise. You can also see all the comments so you can also judge progress.
Ask questions in negative every 5-10 minutes "Does anyone need more time".
Once everyone is ready, start the meeting by going through comments from top to bottom.
After that it runs like a normal N-Pager meeting, or tech review or whatever.
I will say that with say google docs you can use suggestions and other things or say "I'll work on that". And just move on. It's rarely important to rabbit hole on the english, esp on engineering docs. If you're writing a actual PR or marketing doc, sure.
The features I find useful are: - Cursor Position of readers (minor) - Comments - Suggestions (like google docs), helps with minor edits
The rest don't matter. Hell you don't even need suggestions. Comments are really about all you actually need.
Digitally has 2 big benefits: - You can see when someone is commenting on a thing and skip down so not everyone dog piles on the same thing. - In lower level meetings you are very unlikely to have a note taker, so in digital form everyones notes are in one spot. In the paper form of the meeting you either collect / decipher everyone's notes, or you have argue/defend/explain your doc while also taking notes.
Paper is better for: - Keeping everyone focused. You don't pop that laptop until you're done marking up the doc, people often don't even bring laptops to paper doc meetings. - keeping comment arguments from forming in the margin in the digital document.
Some parts of amazon are trying to do it digitally, esp those that are remote.