Is a PTA Personel Travel Allowance really necessary for a US-Citizen from Nigeria to Denmark or Sweden?

Nope, Utter SCAM !!!

No, there is no such thing. This is a normal part of a scam, normally they have already gotten visa and passport money before they ask for the PTA.

This is one of the most famous and common frauds today

So how much money have you lost already? As Fr_Chuck said, by the time they are asking for this travel allowance, they have already gotten the Visa and airfare and usually a few other "monies". Stop sending money. You won't ever see this person.