Yes, it doesn't "break" encryption, it just defeats it.

The client-side scanning means that some amount of your communication will be uploaded in clear text to the government. And unless the government keeps it completely secure (spoiler: they won't) this will leak. Therefore it defeats the point of the encrypted channel.

So sure, it isn't as bad as just removing encryption from these apps. But it is very similar to giving the government a backdoor key to all messages. Maybe you see it as slightly better because only the messages flagged by the automated scanning are made vulnerable or maybe you see it as slightly worse because previously you would need both the backdoor key and access to the original messages and now all of the data you want is in a single location.

But the point is that this significantly weakens the security properties that these E2EE messengers provide if implemented.

I'm not saying it's better because it doesn't break encryption, that doesn't matter, I'm saying we shouldn't be fight it by framing it as an attack on encryption. What I think chat control is, is yet another attempt to force our devices to act against our interests.