I have not seen this addressed much in regression (it is central to factor analysis). Doing this would mean that you end up with predictor variables that are unrelated to each other. While that might make analysis simpler it probably would not be very realistic for real world variables. Generally you are interested in what actually exists, not artificial variables. It depends what you are interested in doing.
Thanks @noetsi, that makes sense. However, now that I think about it a bit more, when we include predictors in the model, say IV1 and IV2, isn't, for example, IV2 partialled out in relation to IV1, such that IV1 reflects unique contribution? How is it possible that variables that are included in a regression model still be correlated if they have been partialled out?