I wonder if the people who believe that they have a correct monitor color profile, make a test with an image using the same file, software, and settings to convert the image to the monitor profile, and then again convert to a common color space like sRGB, then if everyone has a correct monitor profile, everyone should end up with the same image, shouldn't they? No? Do I make sense?
No...what you just outlined is not at all reasonable...
The ONLY use of your display profile should be for Photoshop, ACR or Lightroom to use to display your image–whatever it's color space–to your display. Doing a Convert to Profile to your display profile is, well, to be blunt, ignorant.
Yes, lot's of displays are still struggling to display sRGB (top of the line displays can display real close to all of Adobe RGB). But the purpose of the display profile is really ONLY to give PS/ACR/LR instructions for how to display your image...
When you output the image to ANY output devise (be it inkjet, photo contone or display) only THEN do you do a final color transform from your working space to your output profile–never your display profile.
Your display profile is unique to YOUR specific display at given time and calibration–it is unique.
It's usefulness ends for any other purpose other than feeding PS/ACR/LR for corrections of your image in its working space to your display. The display profile is pretty much useless for any other purpose.
You want images for the web, transform to sRGB. You want images for magazine work (halftone), transform to Adobe RGB. If you want long term archival master images, use ProPhoto RGB in 16-bit.
But your display profile is transient and ONLY useful for looking at and evaluating the image inside of PS/ACR/LR.
Really, forget about trying to use your display profile for anything else...