"Maybe short-term trading is something that can only be done if you have access to a computer all the time?"
I don't think that's entirely true, up until 2 months ago I did all my trading on my iPhone (E-Trade for trading and TD for mobile L2) the only downside is I couldn't see time and sales.. Plus there is a rumor that E-Trade is going to be updating their app to allow L2 and who knows, maybe T&S also :)