It's similar, though in theory you are paying the index fund to act as your agent, and the fee structure is observable.

Regarding liquidity, I imagine it's possible that the index fund might allow you to withdraw money faster than you could sell on your own, but realistically I kind of doubt it.

forget index funds, you could say the same thing about supermarkets. Pointless middlemen!

They are in the logistics and goods storage business. So you actually can't say that about supermarkets.

The classic theory of longer term investing is that you are providing capital to businesses and rewarded for that. That is a little bit different from being a middle man. My personal opinion though is that lending money/investing capital and capitalism in general is power. Money quantifies the potential of making other humans do things for you, it allows you to excercise power over fellow humans. Inheritance means you can inherit that power from your parents. It's not all that different from feudalism.