Yeah, I feel your pain. Screen Time won’t stop them from deleting messages - it’s more about limiting what apps they can use and when.
The thing is, you can’t really prevent deletion on the iPhone itself without jailbreaking it, which creates a whole new set of problems. Most monitoring apps (including Eyezy from what I understand) work by uploading copies of messages to your dashboard before they get deleted. So even if your kid wipes them from the phone, you’ve already got them backed up on your end.
That’s kind of the whole point of these apps - they grab the data in real-time or close to it. If messages are getting deleted before you see them, might be worth checking that the monitoring app is syncing properly and uploading frequently enough.
What are you currently using to monitor?