DELPHI: It's tough to live with people stuck in the past, isn't it? (1.6.37)
Delphi is the villain of the play, both because she wants to resurrect Voldemort and because she kills an innocent boy. But like the play's heroes, she too wants to change the past so she can see her father again.
HARRY: You're fourteen years old now, Albus, and I wanted to give you something which—meant something. This…is the last thing I had from my mum. The only thing. I was given to the Dursleys wrapped in it. (1.7.20)
Harry is still thinking about the past, and he's passing the weight of it onto his son, who never asked for it. The "people stuck in the past" describes Harry Potter with a capital P.
HARRY: I was dreaming—I was under the stairs and then I—I heard him—Voldemort—so clearly. (2.2.9)
Even Harry's subconscious is stuck in the past. His dreams are almost identical to his memories, with a little Voldemort added in for good measure. It's almost like even his subconscious knows that if he doesn't stop obsessing over his past, bad things will happen.
ALBUS: It's a brilliant plan. The secret to not getting Cedric killed is to stop him winning the Triwizard Tournament. If he doesn't win, he can't be killed. (2.4.23)
Literally going back into the past is a terrible idea, but Albus and Scorpius need to experience how bad it is firsthand so that they learn their lesson. It's a little harder for people who are metaphorically stuck in the past to realize how damaging the effects of that can be.
ALBUS: Fine, let's go back—fix it. Get Cedric and Rose back. (2.16.28)
Albus is showing similarities to his father here. Make a mistake? No problem. Take a Time-Turner and fix it. It worked for Harry in Prisoner of Azkaban. Why wouldn't it work here?
DOLORES UMBRIDGE: But in the three days since I found you in that lake on Voldemort Day, you've become…odder and odder. In particular, this sudden obsession with Harry Potter. […] Questioning everyone you can about the Battle of Hogwarts. How Potter died. Why Potter died. And this ludicrous fascination with Cedric Diggory. (3.1.11)
Our search for "Cedric Diggory" on fanfiction.net returned 827 results. There are a lot of people with a "ludicrous fascination" with Cedric Diggory. Why are they still stuck in 2000 when Goblet of Fire was published?
PROFESSOR McGONAGALL: And your response to disappearing Hugo and Rose Granger-Weasley was to go back in time again—and this time, instead of losing two people you lost a huge number of people and killed your father—and in doing so you resurrected the worst wizard the world has ever known and heralded in a new age of Dark Magic. (3.10.4)
Thank Dumbledore that McGonagall is around to discipline Albus Potter. If it were left to Harry, he'd probably tell Albus how cool it was the time he went back in time and saved his godfather.
ALBUS: The stupid thing wasn't going back once—anyone can make that mistake—the stupid thing was being arrogant enough to go back twice. (3.14.22)
Being able to return the past is an alluring prospect. That is why we have so many movies and TV shows about time travel. It's irresistible. Albus and Scorpius have to go back—and screw up—twice before deciding to not to do again. And even then, Scorpius doesn't destroy the Time-Turner right away.
DELPHI: I am the new past. (3.16.69)
Delphi follows this line up with "I am the new future" (3.16.71), but that's almost an afterthought. Delphi wants to rewrite the past. A new future isn't her goal; it's a side effect.
HARRY: Love blinds. We have both tried to give our sons, not what they needed, but what we needed. We've been so busy trying to rewrite our own pasts, we've blighted their present. (4.4.67)
Harry makes a good point in the latter part of his statement. He and Draco (but mostly Harry, honestly) have been too busy trying to love themselves instead of loving their kids. Maybe that's what he means by "love blinds."