Anyone whose ever studied vibrations (e.g. spring mass dampers) already knew this. This is a cool example but it’s not really any more “essential” than macro-level phenomena.
Imaginary numbers are merely convenient in the cases you’re describing; you can get the same results without using them. The paper this article is about is claiming that in QM this is fundamentally untrue, and models that don’t use complex numbers cannot match those that do.
There might be ways around it, but I'd wager that anything you come up with can be massaged a bit to make it look like time is an imaginary dimension of space where it's contribution to distance along the spacetime manifold is negative when squared.
What I see from the preprint (notice that the authors have not discussed it with Quanta, because it is under peer-review) and bothers me is that they "add a real qubit" (...) which should be done very carefully because the two real qubits are not independent (they are linked by the hamiltonian).
I have not read the whole preprint, though.
So it's not that the complex representation isn't a useful mathematical tool, but that it was an alternate representation that was easier to work with. Can you represent a spring mass dampening with all real valued quantities, even if it's a real piece to work with?
e^(-at)*(A cos(bt) + C sin(bt))
where b is the frequency and a the dampening.
(But you might not be asking for an answer).