Okay, first of all, regarding what you've been told about monitor profiles containing "target values," and not the actual "physical values" of the monitor".... Well, I'm not sure we could say it contains either one

Although, it was certainly created using target values (from your colorimeter) and physical values (from you monitor).
Here's the deal... As you know and have done, you calibrate your monitor using a colorimeter and the software that comes with it. Basically, what happens is the software outputs a series of color patches, of known color values, on the monitor and the colorimeter then reads the values that your monitor displays. The software then compares those measured monitor values to the actual values sent to the monitor. Knowing the difference between the actual values sent to the monitor and the values output from the monitor, the software can create a profile of the monitor. That profile can then be used to create an output correction curve (lookup table) that the video card uses to adjust your monitor (hopefully correcting the monitor's output value so it matches the known color values output by the software).
As you mentioned, over time, the physical values of the monitor drift. So, it makes sense to calibrate often in order to allow the calibration software to create a new correction curve.
Secondly, you should not select your monitor profile in that RGB drop-down menu. That's for your working space (sRGB or Adobe RGB 1998) not your monitor profile. Photoshop will automatically use the system's default display profile for the screen display. If you use your monitor profile for your working space, your Photoshop images will look great on your monitor but not on other people's monitors. Their monitor profile is different than yours! You can easily check to see if Photoshop is using the right monitor profile. Just open that RGB drop-down menu you mentioned and look for "Monitor RGB"; the profile created with your colorimeter should be listed there.