I tend to agree with you, despite the famous quotation: "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man")
Science is not a body of knowledge, it is a frontier of ignorance. I like to "feel" that complex numbers are part of the fabric of the universe, if only because it would be more beautiful.
"Clouds are not spheres, Mountains are not cones" - Mandelbrot
Well, I think instantaneous velocity is real, and I think I have a convincing argument. Imagine you have a piece of gum stuck to your bike tire. As your tire spins, the piece of gum spins with it, and its velocity is constantly changing. But when the piece of gum flies off your tire, it flies off in a straight line, following the instantaneous velocity at the moment of separation. Seeing as the gum can fly off in a straight line, its instantaneous velocity at that moment must be well-defined.
If I have 3 match sticks, they are each made of billions of molecules, atoms, electrons, quarks, gluons, etc. So there is no integer count, just in my perception.