Honestly the app is fine, the phone around it is the risk lol. Here is the lockdown routine I run before handing a device to a small human.
iPhone or iPad, use Guided Access: Settings, then Accessibility, then Guided Access, toggle it on, set a passcode. Open PBS KIDS Games, triple click the side button, tap Start. Now the phone is frozen inside that one app. She cannot swipe out into your messages or your camera roll.
Android, use Screen Pinning: Settings, then Security and privacy, then More security settings, then App pinning. Turn it on and enable the ask for PIN option before unpinning. Open the app, hit the recents button, tap the app icon, choose Pin. Same effect.
Turn off purchasing at the account level: On iOS go to Screen Time, then Content and Privacy Restrictions, then iTunes and App Store Purchases, and set In app Purchases to Don’t Allow. On Android open Play Store, tap your profile, Settings, Authentication, and require biometrics for every purchase. The app itself has no purchases, but this protects you from whatever gets installed next.
Kill notifications: Long press the app icon, open App info, then Notifications, and switch them off. Fewer pings means fewer meltdowns when you take the phone back.
Set a hard timer: Since the app has no internal limit, use the phone. iOS App Limits under Screen Time, or Family Link on Android, will cut it off at your chosen number of minutes.
Airplane mode trick: Download a handful of games first, then flip airplane mode on. She plays, nothing loads, no accidental anything.
Five minutes of setup, zero drama later. Do it once and forget it.