You do have influence, you just chose to give it away. Your ETF provider definitely votes in shareholder meetings in your name, using the voting rights which come with the shares they bought for you. If the fund you use doesn't offer pass-through voting or at least the choice of several voting policies, then you've got only yourself to blame for rubberstamping the asset manager's choices.

As to insight: a shareholder having information beyond what the public has is called "insider trading", so that's not going to happen. But nothing is stopping you from pushing the board to release more information to the public. At the moment there's little reason to do so as companies being secretive provides a competitive advantage, which is in the shareholder's interest - but that equation would obviously change when that same secrecy exposes the shareholder to risks of unknown size, and when all companies are forced to be transparent it is no longer a competitive disadvantage.