Yes, lump sum maximises expected returns, but you typically don't want to just maximise expected returns. Volatility matters.
If I give you this once in a lifetime trade: 100k for a 1 in a 1000 chance to win 500M, would you take it? There are very few people who would, even though it has 400k of expected returns, a whopping 400%.
Most of us simply don't make enough money in a life to take that trade enough times to cope with its volatility. Elon Musk should probably take that trade though.
If I give you this once in a lifetime trade: 100k for a 1 in a 1000 chance to win 500M, would you take it? There are very few people who would, even though it has 400k of expected returns, a whopping 400%.
Most of us simply don't make enough money in a life to take that trade enough times to cope with its volatility. Elon Musk should probably take that trade though.