There exist single photon at a time experiments though for a double slit experiment the single electron at a time are easier.
That the interference pattern disappears if one places detectors to check the path is an experimental fact, it is the result of the mathematics of quantum mechanics which up to now really describes the microworld of particles and atoms.
As it is clearer for electrons, I will start with them:
a) There exists a wavefunction a solution of a QM wave equation, which may display wave characteristics of interference given the correct boundary conditions , which pick the solution.
b)The double slit experiment is a boundary value problem for the quantum mechanical regime. It is the boundary problem "electrons of specific momentum scattering off two slits of specific size".
Nature gives the solution as an interference pattern.
If one puts a detector on the path of the electron, the boundary problem changes to " electrons of specific momentum scattering off two slits of specific size and rescattering off detector on the way". Let us suppose that the detector at the screen is an active pixel with good time resolution so only a detector on the way is needed.
What happens is that any detector on the way will scatter the electron, i.e., a different wave function will be describing the setup.The interference pattern is not seen because the secondary scatter spoils the phase of the solution, with respect to the geometry and no interference appears.
That it is the change in the boundary conditions that destroys the phases and thus the interference pattern was made clear in a recent photon experiment, where they show that by trying to locate which way the photon went, the photon reaching the detector loses the phase and leaves the interference pattern.
The same would happen with any detector, either positional or timing detector. The change in the boundary conditions that the detector introduces destroys the original phase correlations that gave the original interference pattern.