The reason why the electron double slit works the same way as the photon double slit and the neutron double slit and the helium atom double slit is because all of these are measurements on distributions of quanta of energy. Energy behaves the same, no matter what kind of system it describes.
What undergoes "superposition" are not the individual systems. Superposition is a property of our theory that describes our uncertainty about their "state".
Think of quantum experiments the way you would think about dice. How does the physics of dice work? Dice can be either resting on the table or they can be rolling. Resting dice show one of six faces. They have zero kinetic energy in the rest system of the table. When we pick them up and we roll them they acquire kinetic energy. Rolling dice do not have a value assigned to them. They have to come to rest, first, which they do by shedding energy through friction on the table surface. Only after all of their kinetic energy is shed do they have a defined value, again. We can't talk about the physical state of rolling dice in the language that we use for their outcomes. We can assign a probability distribution to the ensemble (infinite repetition of the same dice roll) of the dice, though. For fair dice that distribution predicts that we will see a roughly equal number of outcomes for every value on average (law of large numbers). We don't have information about the individual outcome of a throw, but we have a good idea that "3" will appear with a similar frequency as "1".
Quantum systems work in a similar way (but as a warning: the math is different and so are the physical consequences, so the analogy only takes you so far): a quantum system is either in a well defined state or it is evolving. While it is evolving we can't assign a final state to the individual system. It is undetermined, just like the rolling dice. When we make a quantum measurement we take a certain amount of energy out of the quantum system. This is analogous to letting the dice lose their kinetic energy on the table. It's an irreversible energy transfer from the quantum system to the measurement system. The total amount of energy that gets transferred is called "the quantum" (of energy). The numerical amount of that energy determines what we call the new state of the system. If we repeat this process over and over again we can build up knowledge about the ensemble of the quantum system, just like we did with the probability distribution of the dice.
It turns out that the math of the function that describes the ensemble, called the wave function, is similar to that of vectors in a vector space. We can perform linear addition, multiplication with constants and operations like decomposition in base vectors with this quantity. These operations on this mathematical abstract are what gives rise to the term "superposition". This is all well defined, but we have to be careful not to assign this function and its mathematical properties to the individual quantum system. It was never intended to be used that way, just like the probability function of individual dice was never intended to be a statement about a single dice throw. All of these qauntities are ensemble averages.
One of the main differences between the dice example and quantum systems is that dice have their "measurement device" built in by having six faces. We are always performing the same "measurement" on them. That is not so with quantum systems. Here "the measurement" is defined by the external system that absorbs the energy of the quantum systems during the irreversible energy transfer process of the measurement. From that it follows that we can perform different measurements on the same ensemble of quantum systems by changing to a different measurement system. What we can never do is to perform two different measurements on an individual copy of the quantum system. It has only one amount of energy and when that energy is shed in one kind of measurement, then it's irreversibly gone and we can't use it again for a second or third measurement. That's no different from dice throws, again. One individual dice throw can be carried out only once. The next time we throw the dice it's a different physical process, just using the same dynamics.
So what does that mean for your electrons? It means that one electron gives you one amount of energy somewhere in your detectors. No interference. Just one measurement result, similar to rolling a "4" in an individual dice roll. Repeat and a different electron will land somewhere else, just like the dice might now show "2". Rinse, repeat many times and a pattern builds up. With dice it's a pattern of equal outcomes. With electrons, photons, neutrons, helium atoms, cows, asteroids and Porsche 911s it's the same diffraction pattern. OK, don't try it with cows, asteroids and cars. It won't work with macroscopic objects, but not because they don't have quantum behavior. We just can't measure it at room temperature and with the instruments that we can build with our current technology. Point is... the system doesn't matter, as long as we are performing the same kind of measurement on its energy.
