There are three main systems of modern academic ethical philosophy. Each has its own advantages and disadvantages. Only one of these prioritises human rights, and one does not recognise human rights at all as such.
Notice that failure to recognise human rights NEED NOT mean it is OK to do bad things - murder for example. It simply means that those philosophers have different reasons for saying murder is wrong; reasons that do not invoke the idea of "human rights" at all.
So the short answer is that some modern academic philosophers do and some don't. However most legal systems are based on a theory of rights: that bias is not about philosophers but about the people who invent laws. The lopsided bias towards rights is not the only thing you can base laws on: but it was spread around the so-called developed world by European colonialist in the 18th and 19th centrury, as a reaction to ideas like the so-called Divine Right of Kings; whereby what the King ordered was the only criterion of justice. The US Declaration of Independence is the most celebrated example.
So please don't blame philosophers: blame the colonial powers of one or two centuries ago. As a Brit, that includes my ancestors.
But that answer is more about history, law, and jurisprudence than about philosophy. I will return to how that happened at the end: if you are more interested in that than the actual three schools pf ethical philosophy then scroll down.
If that's enough, stop reading this answer here, but thanks for coming with me this far :)
If you want to know about what modern adademic philosophers of ethics think, then read on. By "academic" I mean those who write books on ethical philosophy as a subject in its own right, rather than to underpin some other cause, and that includes what you might study on a philosophy degree at uni.
We talk of good people, good actions, and good outcomes. If these three "goods" always came together, ethical philosophy would be easy. However, we know that good people can do actions we might judge to be bad; or that bad actions sometimes lead to good outcomes. How do we cope with those paradoxical obeservations.
The three schools of Virtue Ethics each take one of these as definitive; and take the other two as depending on the one chosen as definitive.
After describing each of these, I will comment on everyday ethics, which in practice tends to be a philosophical mess, being an eclectic mix of the three schools of academic thought.
Virtue Ethics takes the Good Person as the definitive starting point. Even if an action is one we would often deem wrong, or led to unpleasant outcomes, if it was performed by a normally virtuous person (not under coercion, nor while drunk or insane) we regard the action as being right becasue it was done in good faith out of virtuous considerations. Christians are intuitively using virtue ethics when they try to solve a moral dilemma by asking "what would Jesus do in this situation?". The questionner is a Hindu, and my ignorance prevents me giving an example from that religion: but I am confident this is a part of Hinduism, as it occurs in most World religions. These ethical theorists are sometimes called "neo-Aristotelians" because they adopt some of their thinking from Aristotle, but NOT "Aristotelian" becuase most would utterly reject his own example becasue of his attitude to slavery and to women.
Consequential Ethics takes the good outcome as being definitive. Philosophers have chosen various consequences for consideration, and whatever we choose as our definitive good is called utility. That is why these philosophers are sometimes called "utilitarian" but please do not interpret that as an insult, the way we might treat "utilitarian" in ordinary speech. And notice that it is the intended outcome that is under consideration by most consequentialists, not the well intended action that leads to a disaster by bad luck.
Duty Ethicists take the idea of Good Actions as their starting point. In the most famous example among philosophers, Kant said that we should always treat another human as a being with their own ends; never use them as an object that can be used for our own ends without their desires or interests being considered. Duty ethicists include the idea of rights as a kind of duty: you have a duty NOT to transgress the rights of another. Duty ethicists are also called "Deontologists".
Tip: do not mistake the word "deontology" as the opposite of "ontology (another philosophy term of art). They have nothing to do with each other. The word comes from the Latin "deon" mening "duty".
Academic philosophers love to dream up horrible dilemmas as thought experiments, and I will give you one now to highlight the differences between the three schools of ethical thought.
You are the captain of a small lifeboat, and you have been called out to rescue some people trapped by the rising tide in two inlets from the sea. By the time you get there you realise that time will only allow rescue of one group. Here are some points which some philosophers think are relevant
One group is of 12 people, the other of just three.
The 12 are all strangers to you
The three are your spouse, your father, and your daughter.
You have a coin in your pocket.
Your boat could hold all 15, but a failed attempt to rescue the second group would mean almost certain death for everyone, including you and your crew, as you got pushed onto the rocks by the huge waves.
Which way do you steer your lifeboat?
Consequentialists would rescue the 12: the greatest good for the greatest number.
Virtue Ethiciscts would rescue the three: clearly family love is a virtue, and only a bad person would ever prioritise strangers over family.
Duty Ethicists have the hardest job answering this question. They abhor the idea of preferring the many over the few: each individual has an equal right. They abhor the idea of preferring family for the same reason. They reach for the coin and toss it to make their choice. That way every person has the same, 50%, chance of survival.
As it can be seen, each decision has its merits. Oddly the one that is fairest in mathematical terms, the Duty Ethics one, seems really odd to most ordinary people.
That is because those of us who are not actually studying philosophy tend to jump among the three schools of thought in different situations. With an "academic philosophy" hat on I would say that that is indefensible: we should have a clear way to determine which is which.
In everyday life I do tend to roughly follow all three just as everyone else does; and when the answers conflict I fall back on Virute Ethics to have the casting vote. Usually :(
So, before finishing: I am guessing the real question behind the one that was actually asked is slightly different. I think the OP meant "why do most modern legal systems rely on Rights?". That is because of the idea that a fair system of law should be predictable. That idea sounds obvious, but it isn't -- as the example of the duty-ethics lifeboat captain shows.
In Judaism from the time of the return from Egypt up to the annointing of their first king, the Hebrews seem to have been pragmatic Virtue Ethicists where the respected "judges" or "sheiks" of a village would rule on difficult cases, underpinned by just 10 hard and fast laws (hence a mini-deontological sytem supplemented as need by by Virtue). After they had a king the last appeal of any decision was to the king - an idea that lasted centuries and certainly spread wherever Christianity was the religion of the local ruler.
Before 1066 English law developped similarly, as a mix of Law and "Equity" (related virtue) but the conquest by Normans in that year introduced the idea that Law should be certain: that is I should be able to work out in advance whether my action will be legal or not. That led eventually to most traces of virtue ethics being pruned out of English law over the follwing centuries: to the benefit and dis-benefit of all the former British colonies.
Consequentialism only came in during the 19th Century, and underlies some government decisions (as in cost-benefit analysis when the cost is borne by the taxpayer but the benefit by some of the public).
So most people are somewhat eclectic in everyday life, but in contrast most legal systems (that are not dictatorial) tend to be duty-based. That is why most people, in many countries, often think that the law is a right old donkey.
Citation: the above answer comes after studying philosophy (and law) courses at the UK Open University with course references A310, A427, W200, W201 and the associated course materials and textbooks. However I may well have introduced errors of my own as my studies were some years ago...