|There's more than one way to do things|
I am glad you disagree. Your disagreement hasn't changed my opinion.
First of all learning Latin had a definite use. In an era where every educated person learned Latin, not knowing it shut you out of many areas. And even today if you need to access historical records, it is critical to know Latin. But as I said elsewhere, saying that a subject has a use doesn't mean that it is useful enough that everyone should go out and learn it. Quite the contrary, because of constraints on time we do not learn many useful subjects, and should choose wisely.
It also doesn't mean that your examples are well-chosen.
Law I cannot comment on, knowing Latin may be useful there. But people I have known in various sciences and medicine have told me point blank that learning Latin is not very useful for what they do. Yes, they use Latin-derived words. But most of what they have to know isn't those words, and learning the ones that they need to know is such a small part of what they do that it would make no sense to learn Latin first.
So I have to decide whether to believe a random stranger on the net making sweeping claims about various professions versus accepting what PhDs and MDs have told me about what they do. I would that all my decisions were that easy!
Going further, what you say about various Romance languages (and about English - which got a lot of vocabulary from French in particular) is definitely true. However it is a disingenuous argument since learning any Romance language for the same effort both teaches you a language used by millions alive today and gives you the same head start on other related languages. Which makes Latin an inefficient path to that result.
And that is why Latin is no longer a basic part of our general education. Most of the reading and writing people do is in their own vernacular language(s), scholarly discourse takes place almost exclusively in them, and even Christian worship is no longer generally conducted in Latin (a process that took from Martin Luther to the late 1960's). Given this, learning Latin simply doesn't make very much sense for most people. It held on for a long time based on inertia and general acceptance that somehow someone who didn't know Latin wasn't really educated. Learning Latin taught, so the argument went, "analytic thought". Those declensions had to be good for something!
That proved not to be enough. So eventually Latin was discarded, more useful topics replaced it, and life went on. As with the loss of Euclid's Elements as a basic textbook a few decades earlier, something was lost and on the whole rather more was gained.
PS I know that spelling flames are silly, but I have to admit to finding it ironic when someone who is telling me the importance of developing a better vocabulary gets the spelling of "medicine" wrong...