I’ve got some more information on this: When I right-click the devices in Window -> Devices, "Show in Run Destinations Menu" is checked on all the Simulators just like it is on my real devices, yet only the real devices show up.
Also, I just tried creating a new iOS project from scratch, but there was no option to run anything at all. I don’t even know how to set this up, though, because I use Unity for creating Xcode projects. But I can confirm that this issue shows up on all the Projects that I am working on. So it doesn’t seem to be project-specific.
Besides, when I updated to 6.2, the simulators still worked in 6.1. Only 6.2 was having this issue. Well, and then 6.3 and now 6.4.
In one of my previous posts I answered the problem has been resolved to some extent.
But ultimately I was informed everything on Xcode's side worked as expected.
The bug was Unity-related. There has never been an option to run a Unity build on both simulators and actual devices.
There was a bug showing the simulators even though they were not available.
Now everything works when building for simulators in Unity.