I agree that many meetings of 4+ people can probably be done more efficiently via email or wiki or whatever, but I've found 2-3 person meetings far more effective than any other means for information transfer and decision making.
In my experience, it also depends a lot on the type of information being transferred. There's a lot of information that is much off being expressed in a chat program, where the person can take the time to formulate the best way to express the idea. If the same thing was being discussed in a meeting, it would take the time of everyone there while the person went back and forth coming up with the right wording.
Propose a "memo culture". That was how we managed larger meetings at Netflix (and I'm pretty sure we stole it from Amazon).
Before the meeting, everyone who has a stake in what's being discussed contributes to a memo outlining their thoughts on it. Then everyone reads it ahead of the meeting.
The meeting is then just to hash out what's in the doc and agree on which already proposed solution will be adopted.
I'd caution against memo culture, actually. I only have a sample size of 2, but in two organizations I've been in that tried to adopt something similar, this is what happened:
In the first org, there was a lot of pressure that any such memos had to be highly researched and data driven (also borrowed from Amazon, I imagine). In reality what this meant is that drafting a memo even for the smallest decisions or ideas became a large laborious effort, which nobody wanted to do and/or didn't have time to do it. The result was that everyone procrastinated on decision making, if they even participated in it in the first place, and I knew a fair share of colleagues who didn't even bother to pitch their ideas because of hating the memo system.
In the second org, it was the opposite problem: in an attempt to make memos "painless", there was much less pressure on making the memos "high quality". The result: every "memo" was a hastily scrawled together draft of random notes that didn't make much sense, and we had to spend most time in meetings going over the "memo" to decipher it and have the author explain it anyway.
No one is in charge forever, lead by example and if you’re doing things right eventually people will follow. You are as much a part of the culture as the current “boss”
If you hold a meeting, suggest using a memo? Or just ask your manager if they'd consider it? There are many ways to affect change within an organization.