You can just pick stocks - if you pick a fairly low number of large stocks in broad categories with correct weight, you will track the index.
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.
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.)
With index funds you never have the strong winners to do this with, and so giving is far less tax-efficient.
If you don’t pick the right grocery company, you have a shot at picking the right telecommunications company. You pick fewer winners, but you’re also picking fewer losers.
The real reason to do this is because you want to avoid specific companies that are inside the index. You would only do this if you felt confident in your ability to avoid investing a lot of capital in losers. Even if you’re great at avoiding the telecommunications loser, you might be worse than average at avoiding the loser in other sectors.
Or, I can pick up 100 shares of an index ETF for a few thousand and have someone else do all the work for me including rebalancing and doing all the other required calculations (lot tracking and cost basis calculations etc.).
Assuming you're in the US there are several competent brokers that sell fractional shares. Any broker will do lot tracking and cost basis calculatioms for you, they're required to.
Rebalancing might be a pain, yes. I'd bet the drift isn't too bad most of the time, but it's probably effort every time you add or remove money. You'd want to build a tool to tell you how to add and remove to get closer to the index. If you can get the index weights and your holdings in a machine readable format, it would seem pretty tractable, but it would take time to setup; there's a reason funds have expenses, but index fund expenses are small.
I'm 100% invested in funds because it's a lot less work, but if you felt strongly about excluding certain stocks, I think it's pretty doable for say S&P 500. Tracking a total market index, or an international index would be more challenging. Bond indexes are also challenging to track, even for bond funds.