If by philosophy we mean the most general study of the must general, asbtract or fundamental properties of the world, including as applied to specific key topics or areas of knowledge, then even aside from philosophical questions of ontology, epistemology, aesthetics and ethics, the reason I think that having access to engaging in philosophy proper is worthwhile is that seriously studying philosophy really can help you work on your ability of critical and conceptual analysis and logical argument.
Hard agree. My favorite definition of the field is Wilfred Sellers': "the aim of philosophy is to study how things, in the broadest possible sense of the term, hang together in the broadest possible sense of the term." Some education--and experience in thinking about that stuff--is invaluable no matter what you're doing; it's the field of study that is (or at least can be) most laser-focused on critical thinking skills. I'd never advise anyone to get a PhD in it, but it absolutely should be part of general high school and college curricula, and it's an extremely versatile and valuable undergraduate major.
One consequence of this is that, frankly, I'm not always convinced that the students in their class on, like, Baudrillard are really working on their critical and analytical skills in the ways they would if they studied other thinkers, schools or topics.
Agree again. Teasing out relatively mundane positions from deliberately impenetrable texts isn't super useful for most people, and while it might give you some transferrable skill in exegesis, there are better ways to spend your time. A good philosophical education should focus on clarity of expression, rigorous thought, and careful definition of the terms/groundwork of a problem. Those are all incredibly useful skills, and are invaluable in seeing exactly how fucked up our contemporary economic system is. A good philosophical education will also make you comfortable asking "why" questions about things that are, to most people, just transparent parts of the status quo: it teaches you to be bothered by ordinary things, which is the first step toward awakening from (so to speak) the dogmatic slumber of liberal indoctrination.