I am not going to go into the details of how you do this so as to not spread the cursed knowledge further.

Suits should not show the original ID they were uploaded to your master account on and should instead always show the current character ID.

Its a web address.  If your home address is 10 Sunshine Rd, and you want to be incog, its best to stop telling people you live at 10 Sunshine Rd.  You would give them a different address, like, say, 188 Juniper Lane.

As far as if its viable for everyone to check, yes, every browser, every device, everything you play on shows you this for every image you'll ever see on the internet on every website.  Most things with mice, you right click the image.  Most touch screens you long press the image.

As far as when, I think around 1990 is when URLs first became a thing?

If you don't want to be connected with your past account, then don't use your exact same past accounts image URL, instead, upload a replacement image and it gets a new URL that has nothing to do with all the previous times you used it.

For example, my current image is https://mafiareturns.com/image_cache/29549-profile-1513658206.png

If I died and wanted to be incog, I would not choose to use https://mafiareturns.com/image_cache/29549-profile-1513658206.png, instead I would upload a new profile pic.