Yes, theoretically they can. But most succesful daytraders have already problems to put all their own money in the market as they play very short term. I trade the ES and cannot even invest all my own money as size would become too big. Why should I take money from investors then?
For good traders size becomes at the end the problem as they always grow, but the market does not grow at the same rate.
I guess it depends on the bank roll and the liquidity of what the trader trades. But I don't think a blanket statement can be made that it would be illogical for a trader to do this (trade with other people's money).
