I would hesitate to say there is such a thing as "legal science".

But also not certain about what level of language adoption you are considering. There are relatively few scientists in the world, and most sciences as formal systems of scholarship and inquiry are at most a few hundred years old. Furthermore, many early contributions to many sciences, including the theoretical framework and the practical methodologies, were from English-speaking researchers. This is far from universal, but a very strong component.

Legal systems are often the product of many centuries of history within a region. Legal systems also have very different attributes in different regions. The adversarial system used in the UK and many of its former colonies is very different than the civil code system used in much of mainland Europe or Latin America. So there is a very difficult issue of how to describe legal concepts and procedures from non-English speaking nations to those that use English.

While many sciences are universal - fluid turbulence doesn't change much based on where you are - law is local. It is questionable what advantage there would be by use of English, and the costs are many. There would be a major gap between the legal records that existed prior to use of English and those after use of English. Law enforcement and judicial professionals would be required to learn another language, and there are far more people working within legal systems than in science. How would they benefit from use of English?

If you drive down deep enough, you face the issue of access to the legal system by the people who depend on it. Even within any nation, there is a specialized language and procedural system that is used in the legal system that is often very different to that used by ordinary people, and difficult to comprehend without trained assistance. Introducing an additional linguistic barrier would make access to the legal system even more of a problem.

Even considering legal scholarship that is influenced by science - research on eyewitness memory or on the accuracy of confessions, for example - it may be expected that the scholars working in these areas produce work in English. But bringing that research into a court for use in a particular case would require that the relevant research be explained, verbally or in writing, in the language used by the court.

There is an international community of scientists, and this has been true for centuries. But there is not an international community of legal professionals, and the barriers to such a community are very strong and have very good reasons for existing. I'm not sure what would be gained by use of English in legal systems of nations that do not have a history with that language.

There is no doubt that English is the Today's Global Language. English is currently said to be an international language for multinational communication. According to the world Englishes approach, people learn the language in their own terms and to their own ends and these do not inevitably relate to the USA, UK or any other country of which English is the MT. So, it is not strange to find that there is a new variety of English called legal English, such as Medical English and so forth. Legal English is just like a precise style of English used by the Lawyers in their work.

So, one one side I agree that many legal systems do not have a history with English language, on the other side I mean that these difficulties are partially balenced to the possibility to use the same language in academic meetings and scientific events in general.

For example, when I had legal german course in Germany, into my classroom - in Goethe Institut - the official language of the course was english, because the classrooms put together people of very different languages and countries.

Furthermore, during my visiting scholar period in the Max Plank Institut, in Hamburg and in Munich,  english was the common language to communicate each other with spanish, turkish, brasilian...and German people also...

As a matter of fact (and considering the grammatical point of view), linguistic path dependence is a significant problem effectively, so that too many terms are lost in translation. Anyway, the presence of a common block of terms - the so-called "Legal English Style" - reduces the margin of errors, and the errors in translations.