Here is my attempt at a better explanation.
The VOR signal is read as a phase difference between the 2 different signals, the variable and the reference. Setting the OBS just adjusts what your CDI sees as the zero-in other words, if you set the OBS to 180, and you are on the 180 radial, your CDI gets a signal that both phases are in sync. With me so far?
Ok, good. The important thing to realize is that no matter what you twist on the OBS, the signal coming from your VOR reciever into the VOR head is exactly the same. If you are on the 180 radial, the variable and the reference phase signal coming from the antenna will always be 180* out of sync.
When we hook up an RMI, all we do is steal the VOR signal BEFORE you put any input from the OBS into it. The RMI is set up so that whenever the raw VOR signal (not processed or "resolved" by the circuitry connected to the OBS) indicates a 180* out-of-phase condition, the RMI will point at 360, putting the tail of the needle on 180. This cues you, the pilot, that you are on the 180 radial.
Now compare the Localizer. First, you must realize that dialing in a localizer frequency activates a separate set of circuitry in your nav radio. This works because, as you probably know, certain frequencies are reserved for localizers, others for VORs, and ne'er the twain shall meet.
When recieving a localizer, all your nav radio is doing is comparing the strength of two different tones transmitted on the carrier frequency-150 Hz and 90 Hz, IIRC (also labeled in pilot diagrams as "blue" and "yellow"). When your nav radio senses too much blue, it transmits a "fly to yellow" signal to the CDI, causing a needle deflection. Notice that there is no input of any actual magnetic course into this system. This is why when you move the OBS when navigating with a localizer, it does nothing except confuse your student. Therefore, there is no way for this signal to drive a needle pointing to the station. Even if you did set up a system that had OBS input, your RMI needle would only be accurate as long as you set your OBS correctly. If you set your OBS to 360 on a localizer whose course was 130, your RMI would point at 180 as long as you were on course.
Finally, there is no direct degree measurement on a localizer. This is because of the infamous "700 feet at the threshold" standard. Your RMI would not know how many degrees to deflect the needle, because your nav radio does not know how many degrees wide your particular LOC course is, just how strong the "fly right" or "fly left" signal is.