That directionality is very useful. The directionality of a muon or electron produced from a neutrino interaction is correlated with the direction of the incident neutrino. That's interesting for the astrophysical kind of questions that IceCube is addressing, and it's also useful in other contexts (background rejection for fundamental physics searches, monitoring of nuclear reactors via neutrinos, ...).
Cherenkov radiation is indeed polarized, but to my knowledge that hasn't ever been made use of.
Tangentially: there's also some really cool work being done on detectors which utilize both Cherenkov and scintillation light at the same time, exploiting the directional (and other) differences to extract the most information possible out of each event.
There are very good illustrations of this if you search for "Super-Kamiokande Cherenkov ring." That's a Japanese neutrino telescope with a bunch of huge photomultipliers lining the walls of a giant underground cistern filled with water. Ice Cube has similar light detectors, probably from the same Japanese manufacturer, that were lowered on strings into wells melted into ice.