I want your opinions on how useful it is to throw second quantization at students when they have not understood first quantization.
My opinion is that it might not be very useful, but you do need to give a correct answer.
I tend to add a simpler answer when I see this.
That's understandable. If it's a simpler version of the correct answer who could possibly object? I think the issue comes if you start getting sucked into "lies to children".
Also the emphasis on second quantization and statements of the type "all space is filled with electron fields/particle fields etc" instead of "one can describe mathematically that the ground state of the electron wave function covers all space" gives a false "aether type" impression.
It isn't false. Einstein talked of space as the aether of general relativity, check out the arXiv, and see what Robert B Laughlin said here about quantum vacuum:
"About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo."
False because if there is no electron at (x,y,z,t) the ground state gives zero probability of finding one, and the impression given is that there exists something there except zero.
There is something there. Space is not nothing. What's false is the notion that the electron is a point particle located at (x,y,z,t). It just doesn't match the hard scientific evidence of electron diffraction etc.
It is a similar conceptual problem as with virtual versus real. Creating this aether of all fields in mathematics does not mean a real physical existence.
But space exists, gravitational fields exist, electromagnetic fields exist, and so on. It doesn't mean to say that electric fields and magnetic fields exist as separate unrelated things. Or that photon fields and electron fields and gluon fields etc all exist as separate unrelated things. But something exists. See Einstein talking about electromagnetic and gravitational fields in 1929: "It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds". According to Einstein, a field is a state of space. And how many states of space are there where an electron is? One. IMHO little things like this are the key to unification, and the multiple fields of QFT are pulling in the wrong direction.
One can fit the shape of my computer with a Fourier series expansion or another complete mathematical series expansion from here to infinity. This does not mean that part of my computer is at infinity. It makes mathematics as a reality, which is not the current physics point of view imo.
IMO some people elevate mathematics above reality, and don't pay enough attention to the scientific evidence.