If you pick stocks with the correct weight to track the index, you're effectively running an index fund. And so you don't have to rebalance to keep tracking the index.
Indexes rebalance frequently. The "correct weight" today, won't be the correct weight in a year.
What are you talking about? Those index fund are constantly rebalancing. This is why you buy an index fund, so you don’t have to constantly rebalance your portfolio.
1 If you never rebalance, you're never adding new stocks to the index, nor removing stocks that do not belong to it anymore.
2 You need to rebalance to take corporate events into account: new stocks, buybacks, dividends, etc...