Imma be frank, common law is amazing.

It is dialectic, improves on itself over time, and is far superior to civil law. The issue primarily is how precedent is dealt with. Modern courts are bound to interpret fact patterns and legal issues only within the context of the specific cases they get. As such, if the incorrect arguments are made or the facts don't lend themselves to being new precedent, then precedent won't be changed. This is why some legal firms literally try and seek out specific cases with specific fact patterns to challenge legal precedent by taking the case to the Supreme Court (though this is super expensive and many clients don't want to go through the process). While this isn't horrible, it is dreadfully slow. Just as well, most cases which could make new precedent are settled out of court (within the civil context) and are pleaded out (within the criminal context). Only about 10% of cases in either civil or criminal law actually go to trial and are litigated before a judge. So the normal avenue for changing precedent within the judicial branch is pretty slow just based off of case volume and cases actually heard.

Precedent is an interesting topic though. At the district court level (where most cases are heard), an attorney can justifiably use precedent from the state appellate courts, the state supreme courts, and the federal appellate circuits they reside in, even if it contradicts with other appellate level precedent (these contradictions are called "circuit splits"). Supreme Court of the United States (SCOTUS) precedent is always controlling so when SCOTUS comes down on an issue, that is effectively an end to the squabbling between the various appellate circuits. As such, it can take awhile for a case with a precedent challenging issue to make its way through the various appellate circuits, create a circuit split, and provide an avenue for SCOTUS to hear the case. Just as well, SCOTUS only hears a handful of cases every year and they get to choose which cases they hear, so effectively whatever precedent SCOTUS wants to focus on will be the only thing heard.

That being said, precedent and the common law generally are terrific ideas because it allows for the law and the judicial branch to be organic and adapt to changing times. Whereas the civil law is codified before hand and doesn't allow for courts to stray from the black-and-white legal reasoning of the legislature. Further, common law is not only modified by precedent. The legislatures, both state and federal, are primarily responsible with codifying laws and some standards the courts use to interpret facts, laws, remedies, and sentencing. Just as well, legal scholarship is huge (though costly and time-absorbing) in changing the law. Law reviews, legal restatements, critical legal theory, and general legal scholarship are some of the main drives behind changing precedent at the judicial and legislative level. SCOTUS and appellate circuit courts routinely cite to legal scholarship in developing their views on topics of frequent review or precedent changing issues. Again, this allows common law to be organic.

Okay so this is a lot. Effectively, common law is far more organic than its other cousins. Common law allows for courts to be more than just blindly applying the law to the facts and nothing more, it allows for them to interpret law and apply it to the facts. This interpretation allows for the law to change and shift to create more justiciable and equitable outcomes. Common law is a great concept and so is precedent, however, in the hands of the bourgeoisie that created it, it is their class weapon and not a people's legal structure. Law, as is in civil law regimes, should not be a rigid structure to be blindly followed based on the squabbling of the legislature where the judicial branch cannot interpret or critique the legal framework they are given, instead the law should be an organic device where the people who apply the law have some say in how, why, when, and where the law should be applied. As such, the common law is far superior to civil law. Just as well, the common law offers the best area for the development of a truly socialist legal structure.

A socialist legal structure would likely have precedent, multiple levels of courts, judicial branch review of case law, statutes, and litigation in court. Even more, these things would be allowed to organically develop into tools to shape society at large into something better. Where the current common law regime seeks legitimacy from the Constitution, a socialist one may seek legitimacy from the Dictatorship of the Proletariat and arbitrating class dynamics. Where the current common law regime is enslaved to settlements out of court and pleadings, a socialist one may seek to litigate far more cases (just as well the American legal system is woefully underfunded which is why many courts are literally falling apart). Where the current common law regime requires finding vehicles to change precedent, a socialist one may develop a strategy in which to directly challenge problematic precedent without a vehicle. These are mere speculations, but the common law regime, generally, is the best building block for which to build a new socialist legal system.