I don’t think Voldemort cared much if the blood line would continue when he was gone. He was terrified of death. His intention was never to die.

Then, I don't know. I am not Voldemort.

That's what it says on the Wiki page.

It doesn’t say anything about preserving the blood line in Cursed Child. That’s probably just speculation to explain one of the dumber parts of the play.

Also, Voldemort wouldn’t want to preserve the Riddle line. The Riddles are an old muggle family.

And Delphini never got to see her father, cuz he was killed by 'Pottah'.

The whole play is stupid.

Then, why did Voldemort want a child?

Explain that.

What he didn't like about his family is his family was their Muggle blood. Remember, his goal was to eliminate all Muggles and Muggle-borns. Since he was a half-blood and Bellatrix was pure-blood, having a half-blood child wouldn't be half bad. He probably wanted to start anew, since all his relatives are dead.

There's several reason why Voldemort would want a child. First, it could have simply been a reward to Bellatrix for her services and loyalty. She would definitely see it as the greatest honor.

Second, a child would make for a valuable and powerful supporter for him. That will be greatly beneficial in many ways.

Third, we know how obsessive Voldemort is with immortality. Many people in some ways view having children and continuing their bloodline as a way of being "immortal". If Voldemort's Horcruxes did fail somehow, having a blood heir to continue his legacy would be something Voldemort would find appealing.

Fourth, it's perfectly possible that Delphi was an "accident". Based on the time of her birth, she must have been conceived shortly after Dumbledore's death, so it's plausible to think that Voldemort and Bellatrix were "celebrating" his demise. I'm sure there are wizarding methods of contraception, but with as crazy and obsessive as Bellatrix is with Voldemort, I could see her allowing herself to get pregnant without Voldemort knowing, and then presenting her pregnancy to him as a valuable tool/asset. More likely than not though, it's the first three points I mentioned.