If one portrays their character in Oblivion and Skyrim as the same, then why couldn't that character wear the Amulet of Kings? If he was the same one for even more games, surely someone would recognise him. And if you played him as a heroic character, then why does he keep getting arrested?
Two ways around it. First, you just never tried it on, out of respect or it just never occuring before its in the hands of Jauffre. Second, perhaps it is just attuned to the line of Kings or the Septims. I went with the first. As an old friend of Uriel (Arena and Daggerfall) my character respectfully took care of the amulet and had no desire to try it on. You only find out you can't if you try; therefor therefor since my character didn't, the game mechanics will never matter. "You, i've seen you, let me look at your face." Takes ona whole new meaning, as does the faith the Emperor has in you to stand against Dagon. Also, mods. =P
Recogniton? Roleplay it and blame it on game limitations. On the other hand, in Morrowind you only passed through in Arena, you never go back to Daggerfall, and in Oblivon there has been all the tie between Daggerfall and Morrowind since you have even been in Cyrodiil. I have Ocato recognise the character, but thats not until the end of the MQ.
Second is more fun. Arena, the original reason, Tharn. Daggerfall she was the only one Uriel trusted. Morrowind, she chose to betray the Empire and gave the Underking the Totem and a letter from Lady Brisenna arrived before I reached the Mantella. In Oblivion, Helseth could have betrayed the Nerevarine - but I personally chose to use an alternate start mod and winded up in that fateful jail in the middle of a TG mission. Skyrim is after 200 yeras of trying to live a subdued life.
Its pretty easy to do really, more so on the PC snce you can 'fix' the ability differences.