It's only a dichotomy if you see it from the angle where data is sacrosanct and its beset on all sides by evil trying to do it in.
The better way to approach this issue, long term, is from a legal point of view with an interim state where encryption holds us over. That is the law decides who may or may not own or access a certain type of data with penalties upon tort or criminality. And we develop civil protocols for days governance between people and between people and governments.
Like trademark. You could have it so trademark, i.e. authentication, is protected by mathematics, or you can have it protected legally.
Personally I don't believe the answer to data theft or surveillance is more mathematics in the form of encryption, but sensible laws regulating data its, use and access with penalties for transgressing. Obviously this would require international cooperation and would be a long way off and in the interim we'd need encryption to protect against unauthorized access until we reach that state of data governance. But ultimately the answer is not "make everything s black hole".
We don't protect against thieves by building impenetrable houses, we rely on legal instruments to dissuade burglary.