From what I'm familiar with early exercising ITM options with a little or no premium in them, is that back in the day (and I don't know if things have changed or how), is they could be exercised after the close of the stocks/index but before the futures close (now they essentially keep trading though.) So if the futures tank after the stocks close, it would be an opportunity to sell the stock or index at that closing price, and arbitrage that with the futures price (or come in shorter the following day.) So the person getting assigned would be buying the stock at the previous day's closing price, which could be a huge disadvantage if they've tanked since then.
Back in the day tho, there was only a 15 minute window for a trader to make this decision before the exchange had to be notified of one's exercised positions. On also would gauge whether or not to exercise one's long options based on anticipating of getting assigned on other short strike positions, to try and balance things out, but that was always a guessing game.