Today there needs to be a lot of leg work to trace money between institutions. With bitcoins all you would need to do is have a record of address holders.
They would need the same amount of leg work to trace transactions happening on free addresses. Actually it would be much harder, since there would be no institutions cooperating.
It would all be a question of how easy it is to live using more undeclared bitcoins than declared ones. That could work as a double-edged sword for big corporations actually, as people wanting to spend undeclared money would turn to smaller business who don't collaborate with government.