Fiber is so cheap it's common to bury lots more than you need and just leave it for the future. Conversely receivers are not cheap, so you don't want to add unnecessary complexity if you don't have to. Since the goal is to send as many bits per second for the lowest cost, you typically just use more fiber, especially for "simple" systems.
To answer your specific questions:
Why can't simple optical communication systems transmit and receive light of a single wavelength in parallel?
They can, but why would you? What problem would that solve? Fiber is very, very cheap, and if you can't use two fibers, then crude forms of WDM are very cost effective.
Why doesn't the same problem occur when using multiple wavelengths (e.g. in Wavelength-division multiplexing)?
You are really asking why WDM is cheaper. For "simple" systems like these 10gbit SFP+ transmitters, adding WDM as opposed to using two fibers increases the retail cost by $1.00:
https://www.fs.com/products/42306.html
WDM can be that cheap because the multiplexing in this case is performed using lasers with widely spaced wavelengths, so simple color filters can be used. These are very cheap (cents) and cheap is what matters.
Conversely, to use the same wavelength, you need a circulator to sort light by direction. These require first that the light be polarized (or else you need two circulators), and further require magneto-optical materials and strong magnetic fields. Polarization is expensive. Magnetics are expensive. Color filters are not.
How does Direction-division multiplexing solve that problem?
I've never heard of that before, but the webpage you linked more or less provides the seller's answer to this question. They describe a system for low cost ISP networks where the ISP has a single laser on their end. The user doesn't have a laser, just a circulator, which they use to extract the laser beam, read any signals on it, then apply their modulation, and then send back modulated beam. The cost savings is that the user has no laser and is just modulating the ISP's signal back to them. Note that since there is just one laser, you are still limited to only one end talking at a time.
Allegedly this is supposed to be cheaper because there are fewer lasers, but lasers are not expensive. Presumably the vendor has some trick to make the circulator cheaper. Possibly with enough power the "circulator" could actually just be a beam splitter, which could be very cheap (and very lossy).
One answer mentions "reflections" as a problem preventing full duplex, but it is missing a more in-depth physical explanation and some credible sources.
This heavily depends on the situation. If this is a fixed fiber link, and I'm fusion splicing the fiber, I can get the reflection down to a tiny fraction of a percent. Further, if you have a coherent receiver (like the Direction-division multiplexing scheme you linked above), the reflections don't matter anyway since they're not coherent with the receiver and are not detected.
Conversely, if this is an ethernet fiber going under someone's desk using incoherent detection, and they're not polishing and cleaning it after each insertion, then their finger print on the fiber face might mean a quarter of the laser power is bouncing back into the receiver. That would be a problem.
