Does SCOTUS fit into this hypothetical?
One, quick example: You can have appointed experts who can be recalled by public input but never have to campaign for election. I'm writing this in short minutes with zero research so be assured there are countless possible systems that exist in the infinite space between the two binary options implied by your dilemma.
In other words, being elected to office is not the advantage of congress. The advantage we seek is public accountability. Public elections are a pretty fucking poor proxy for accountability though because we end up with single-issue voters acting out of rage and electing people who are specifically inept at their job.
Some people say "if you're not cheating, you're not trying" but this is even a level removed. This is a perfectly legal move that they've denied themselves for no material reason.
Not to mention that packing the courts could well be interpreted as an open attack against the separation of powers
With a populace that cares about ethics and morals, that would be a sensible strategy, but unfortunately about half the voting US population doesn't give a flying fuck about either any more.
Additionally, the danger for Democrats going for low blows and breaking tradition is that they might lose a significant part of their own voters as a result.