To my understanding, "common-law" technically refers to the body of precedent that the United States grandfathered in from English jurisprudence and prior colonial practice into the new United States government, as opposed to "precedence", which is the general principle by which prior rulings at the right scope are respected like statutes are. But that's just a semantic quibble.
But on the question of the weight that precedence carries: I'd be curious how you feel about federally enforce integration of schools as a result of Brown v. Board of Education, or abortion as a right thanks to Roe v. Wade, as two examples of seminal increases of rights resulting from the heavy role of precedence.
Personally I'm a bit of a hybrid in my own opinion. I'm partial to the sentiment that the legislature is the supreme branch of the Government, being the representatives of the people. So in principle, I'm opposed to drastically new doctrines arriving by way of court ruling, especially when they seem a little too "creative" and go outside the scope of interpreting existing law and statute into the territory of what "ought to be law". I prefer that such significant changes be a matter of federal statute, or when they're a matter of novel constitutional interpretation, that they originate in actual constitutional amendment. (Though even then in the case of federal statute, there are very real questions about how and when the federal Congress may override the states, and jurisprudence/precedence has been an important part of working out those questions).
But on the other hand, I am strong a believer that once a court with sufficient scope and jurisdiction has ruled, and a further appeals process is either at a dead end or would be too injurious for various reasons, then upholding the rule of law is of preeminent importance to the stability of society against the breakout of violence or factionalism. So, for example, in the case of Roe v. Wade, I feel the ruling was far too creative and far too tenuous in its actual references to the Constitution. Nevertheless, it is now the law of the land, and if I want the other protections the government provides and protects for me, I feel it would be hypocritical to flout that law just in the cases that I prefer. I actually feel that the outcome of Roe v. Wade was morally egregious; but I won't rebel against it or seek redress outside the established legal order unless I feel ready to morally take responsibility for the potential consequences of anarchy or of violence outside the civil order. Of course, not every question of civil disobedience is realistically divisive or pervasive enough that civil war is likely if I or others rebel. But civil war and anarchy can be the product of a thousand cuts, as it war, and if I had to oversimplify and take it to an extreme, I would say that I do not feel morally justified in flouting a nationally established law unless I feel sure that even the risk of widespread death and war might be warranted. Even with ongoing inequities and injustices (sometimes severe and chronic) in American Society, I still personally feel we generally (generally!) enjoy such a magnitude of protection, liberty, and privilege in this country, and I'm not sure that risking that is truly moral on the balance.