Producers use EQ to shape sound generally, but I know a particularly useful feature of EQ is the ability to cut frequencies that are unwanted. For sounds that are created/designed digitally, though, is there any need for EQ? Are synthesizers and other electronic instruments already "EQ'd" by their very design?
Yes there can be a need for EQ on electronic instruments when recorded.
Yes, synthesizers and other electronic instruments can already have some form of equalization applied internally, but the design of that EQ only considers that instrument in isolation, not in combination with other sounds.
One of the most important functions of EQ while mixing (and mastering) is to make the combination of all of the sounds work well together, throughout the whole piece.
While there are ways to have EQ done entirely by the instrument in question (especially if it's totally "in the box", i.e. a plug-in), it makes more sense to have it done by the mixing system (console, DAW software, etc.) so that a uniform method is used for each instrument.