Well yeah, from a mathematician's point of view, just simple ODEs and PDEs have been studied ad nauseam for so long now, that you have to go way higher to get on the cutting edge of REAL mathematics. But I was speaking of people that go into a field that requires math, and those people are usually not going to be applied/pure mathematicians, but rather ChemE, EE, ME, Civil, BioStats, etc and for those people those courses are going to be the foundations of what they need to practically do in their fields.
Also not sure I agree arithmatic and algebra are on the other side of calculus! Calculus is still more advanced than those, even though we dont fully understand them when you do them in high school. After all, once you understand metric spaces and all that, then you're really ready to re-do your calculus and have some fun with Riemann Stieljes Integals and the like.