I'm A Banana
Potassium-Rich
To make this work you'd have to get rather meta-gamey with the restrictions, and then people would complain because the vorpal sword can't decapitate dragons or jabberwocks.
Well, clearly, jabberwocks should not be solos under this model.

But actually, the reason is justified in the story. Why is that Dragon an elite or a solo monster in the first place? Because it is insanely powerful, a creature that no lone warrior could take down on their own. It ties itself so strongly to life that even a vorpal blade cannot behead it. It is the exception to the rule.
You could even add a secondary "megadamage" effect -- something like, when you roll a 20 and fail to decapitate the enemy, it still deals 4 x damage or something maddening, to show that it TRIED to cut off the enemy's head, but FAILED.
That's all in the details, though. The big point is that an "unbalanced" effect like insta-death can be carefully balanced through a variety of factors, and even if it IS unbalanced (even if the vorpal sword could behead solos and elites!), that doesn't mean it's not fun. It just means the DM should be aware of how that weapon breaks the game before he gives it to the party, so that no player is ever caught with it unless the DM intends for them to be.
After all, in this model, DMs are in control of magic item distribution, and the DM can give you unbalanced magic items and take them away again without ever having to consult you -- magic items are extra. They are not an entitlement. Easy come, easy go.