I have just spent time tracking down the father of an illegitimate baby born during WW2.
My cousin received a letter to say his father had the same name as the baby's father and DNA showed it was someone in our general family. I'm the family historian so took on the task. We were lucky as another of our cousins had his DNA test on the same site and he was assessed as 4th - 6th cousin - not my uncle's child because that would be a 1st cousin.
I found another with the same name in our general family at the correct distance to me using my cousin's DNA result - after a DNA test by that person's son it was found he was a more distant relative than my cousin. The son knew he had a half sibling somewhere.
I advised the person that the DNA should be put on as many free sites as possible and gave the links, this would mean my DNA could be checked against the person's DNA. I map my known relatives DNA to help me. The person's DNA appeared on 2 of my sites and was assessed as a 3rd - 5th cousin and a 2nd - 4th cousin. I mapped the person's DNA where they met mine and was surprised to find they dropped into the area of my gt gt grandmother's DNA. This meant the person's father was a descendant of my gt gt grandparents and the person was my 3rd cousin.
There was only one with the father's name on that line born in the right era and his granddaughter was approached. The granddaughter's aunt had the answer, her parents had married pre WW2 and she and her eldest brother had been born before her father joined the army during WW2. There was an affair whilst the man was in the army and a baby born. He then came back to his wife and 3 more sons born. Only the 2 eldest knew of the affair and baby. The aunt then named the mother of the baby - we had the father.
Without DNA how would the person have found the right family to start to look for someone of the correct name and then prove it was their father? DNA has proved my paper trails which made the cost worth while because I have 4 lines back to the mid 1700s that are now known to be correct - that's priceless as far as I'm concerned. I'd tell everyone serious about family history to consider DNA to use it to prove your tree. One proviso - wait for the offers.