In the double-slit experiment, why is it never shown that particles may hit the space between or outside the slits?

"Is it because they are just simplified illustrations?" you ask. The answer is simply: yes it is because they are simplified illustrations.

Furthermore, not only can the particle hit the barrier outside or between the slits, typically most of the particles do that. Only a small fraction make it through. I say 'typically' because in such experiments we don't normally bother to set up the optics (whether for photons or electrons) so as to restrict illumination to only the two slits and not the surrounding area. But in principle it could be done, and then only a few particles would miss the slits.

It is quite common, in experimental physics in this area, to do what is called 'post-selection'. That is the name for the practice of selecting from your dataset only those outcomes triggered by some signal, such as, in this case, the signal that a dot appeared somewhere on the final screen. Then after that the discussion is really saying not 'this is what happened in every run' but 'of those runs where something made it to the detector, this is what happened'. One can regard the simplified pictures as showing what is understood to have happened for those runs which were singled out by this 'post-selection'.

If you look up Doctor Quantum on youtube you'll find some (horribly dated) 3D animation videos that DO show the particles that bounce off the space outside the slits. At least initially in the 'marble' demonstration (the first light one also shows illumination on the slit device). They are culled later because of the same reason they've been culled from other examples of the double slit experiment.

And that reason these particles aren't shown is because they are irrelevant: they don't pass through the slits and so are not part of the "what happens when they pass through the slits" experiment.

Its kind of like asking why people under the age of 18 aren't included in election polling data. Surely these people exist!

When I performed this experiment the last time, I used a laser, so no single photons were fired, but an endless stream of photons, so to say. Then, the double slit was so positioned that the maximal intensity way measured at the detection screen (with a photometer).

That some photons hit the area between or outside the slits is very likely, as the laser itself has a certain cross-section. Then, the wave-function would collapse or the photons are reflected and therefore not measured.

In theory, if you perform this experiment with one photon, what would you expect? Well, your wave function should include the possibility of a reflected (or not visible / detected) photon with a non-zero probability. Then, an experiment on it would only make sense with many many measurements, to have a reliable statistic for you probability-distribution, so you end up with doing the experiment many times.