Both parties would try to influence the ideological make-up of the judiciary. Back in the good ol' days when the filibuster was used with some modicum of restraint, this meant that a minority party could prevent over-ideological candidates from getting elected. But, over time, the process evolved to the point where the party out-of-power would try to block all nominations so that when they were back in-power in several years, they had more vacancies to fill with their own ideologically-pure candidates.
Purely in terms of government fulfilling its obligated duties to function, this is an improvement because the judiciary will now become staffed. However, the lack of a filibuster threat will probably push us away from politically neutral appointments, towards an alternating (and hopefully balanced over time?) mix of biases in opposite directions.
tl;dr this is why we can't have nice things.