We already have that tradeoff. It’s called a warrant. If the police get one, you are forced to give them access to your otherwise-private affects.
This is a step beyond that. Warrants are granted at the discretion of a judge, the bar is high, the scope is narrow and you (theoretically) have recourse if it’s abused. Here, the discretion is Google’s, the bar is nonexistent, the scope is unlimited and you have zero recourse if you think you’ve been wronged.
This wouldn’t be an issue if people trusted Google or the police. But they don’t, and it’s pretty easy to imagine ways in which this could be abused to harm people.
Let’s say you live in Texas and get abortion pills in the mail. If the police have a warrant to search your house for something unrelated, they (theoretically) can’t see the pills and decide to charge you with an unlawful abortion (unless they were “in plain view”, etc). But if Google gives police access to footage of your house extrajudicially, police can use anything they see as evidence against you. And make no mistake — things like that will happen as a result of this policy.