Since the U3 and U6 more or less follow the same trend., it makes sense to keep using the same reported measure for continuity. People know that 8% "umemployment" (aka U3) is bad. If you suddenly start reporting U6, people will think a 8% U6 is bad, when it is rather good.

If you want to use it to measure or model something else, you might have a reason to pick a different measurement.