Actually, long ago back in ancient times like 2004 or something, I had an old Verizon flip phone that could do this. But it only worked for other Verizon phones. If I texted someone who was also on the Verizon network, there would be a little yellow page that would appear, letting me know if they read my message or not.
This is available today but I think that it requires your carrier to cooperate. If you were to create such an app, you'd have to get all of the carriers to agree with you and let you use their network to determine if this person read the message or not. Carriers can know when you read a text message.
My dad is on the Go Phone plan for AT&T and uses a flip phone and they charge him every time he simply reads a text. If he receives a text but doesn't open it, he isn't charged for that text. That was the same with my Verizon phone. If I opened a text, I paid for it. So carriers do have the technology to know when you read texts...you just need them to cooperate with you if you'd like to create such an app.