It doesn't eliminate the need for the fund to rebalance, because of companies moving in and out of the index criteria.
But it certainly vastly reduces the need of the fund manager to trade.
(Also, stock buybacks and new share issuance should in principle not change a company's index weight, but in practice they sometimes do.)
2 You need to rebalance to take corporate events into account: new stocks, buybacks, dividends, etc...
500 shares of company A is worth 100% of the market cap of company A.
500 shares of company B is also worth 100% of the market cap of company B.
So if you have 5 shares of each, you'll have 1% of the market cap of each, even if one of those companies finds the cure for cancer or turns out to be a money furnace.