Why I would always suggest recording the stack as well as the DI is simple: you can't tell from a DI track sometimes whether a distorted section has been recorded the right way. In that sense, you are flying blind while doing the recording itself.
Better is to record the stack or master mono/stereo as well. That way, when you listen back, you will have an idea of whether you played a part accurately. Sometimes a DI track won't be suitable for that, for example during fast playing or palm muting or complex melodies.
Some good points. And tracks are cheap these days.