From the given information it's a little hard to deduce what you want. But say you have a time dependent magnetic field interacting with a system of particles. Then the spin state of the system of the particles will be time dependent. Therefore, the Hamiltonian will be time dependent. Usually a time dependent Hamiltonian comes from a non-conserved system (here we observe only the system of particles interacting with the magnetic field, rather than the whole picture, which would also include what is generating the magnetic field). Since we ignore what is generating the magnetic field, then the system is not conserved therefore the Hamiltonian is often time dependent.

That's why it is used without hesistation. It's all about the context of the problem.

From the given information it's a little hard to deduce what you want. But say you have a time dependent magnetic field interacting with a system of particles. Then the spin state of the system of the particles will be time dependent. Therefore, the Hamiltonian of the system of particles will be time dependent. Usually a time dependent Hamiltonian comes from a non-conserved system (here we observe only the system of particles interacting with the magnetic field, rather than the whole picture, which would also include what is generating the magnetic field). Since we ignore what is generating the magnetic field, then the system is not conserved therefore the Hamiltonian is often time dependent.

That's why it is used without hesistation. It's all about the context of the problem.