Not sure how influential you are, but one thing I've noticed is that when meetings start to feel unproductive, its due to one of two reasons.
The first is when you have NxM meetings. What does that mean? Well, you have, say, N people representing one interest, and M representing another. You put them all in a room together. This usually only happens when a decision has to be made, and it sucks (note: it's fine if you're just brainstorming, where no decision is being made). This is a great place for leadership to exist; if instead you take the lead from N, and the lead from M, you reduce it back to a 1-on-1 meeting, and then each of those individuals can go back to their teams with what was decided, and have 1xN and 1xM communication.
The other instance is where that 1xN or 1xM meeting feels unproductive. Note the nature of these meetings - they are mostly informational. They're either getting information to inform a future decision (and possibly decide on what the team's position is depending on how egalitarian the org is; I still consider these an informational meeting, since then the leader is more a representative, and trying to find out what the group believes, in order to represent it elsewhere), or they're communicating that a decision has been made. These can likely be done via some asynchronous mechanisms rather than meetings, to avoid it feeling like an unnecessary meeting (and to have documentation of the information!). If it is done as a meeting, be aggressive with providing an agenda, and ensuring only members of a single team/department/etc, and ideally hierarchy level, are included. If you have more than that, you almost assuredly are having a meeting that is 1x(N+M+...), because you're including multiple groups. And those groups have different priorities, interests, etc, and at least part of your meeting is almost assuredly going to be boring and unnecessary for them.