I think people should get in the habit of deleting all their convos that are more than a month old. Most convos are 99.99% worthless, and it's very freeing to be rid of them.
One of my friends had her H1B cancelled and was given a 10 year ban from entering the US because of her text messages. When she crossed the border back into the US, the border guards requested her phone, and searched it and found messages to her ex-bf about marrying him for a green card. She was joking but it didn't matter and she had to fly back to her country of origin that she didn't live in since she was a kid. Since then, even though I don't have anything to worry about, as a habit I delete all my apps except iMessage and delete all my conversations there.