I read an article recently by someone who heard a father say, I don’t understand why my kids are so serious and somber. The author of the article had noticed this too — the father’s kids seemed withdrawn and never laughed and played like other children. The author asked the father, Do you ever tell them stories? He said, Yes, I tell them stories about gedolim. The author suggested he treat them like kids, and tell them stories about princesses and kings and such. Like someone said above, kids need to be kids.
On the other hand, it can be positive for kids to hear stories about gedolim and tzaddkim. Rebbe Nachman of Breslov, who was the great-grandson of the Baal Shem Tov, attested that hearing stories about tzaddikim as a young child inspired him to put in the effort in Torah study and prayer to become what he became.