Seth Masket explains why taking party labels off the ballot reduces political accountability:
[T]here would certainly still be a “party line” in the Congress, even under Nebraska rules. Would such rules reduce the incidence of party line voting? Almost certainly. But keep in mind why this would happen: because it would be much harder for people outside of Congress to follow what’s going on and to assign rewards and punishments. Most voters, even the politically interested ones, generally don’t follow what individual members of Congress are doing. Votes on committee reports and legislative amendments and procedural rules are often strategic and inherently confusing for outside observers. What voters can observe, however, is the behavior of a party when it’s in power. If they don’t like the way things are going, they can vote in another party and get a very different result. The knowledge that voters will reward them if things go well and punish them if things go poorly creates an important (if limited) constraint on legislative parties. It helps make them responsible.