But they're not asking for that. They're asking for the ability to force companies to grant them access to information without something terrible happening.
The only way you could prevent something terrible happening, and have that prevention be "connected to [their] ability to access information with lawful authority", is to have the ability to inspect private data. And the only reasonable way they would do that is to do it surreptitiously.
They could try just asking the user to unlock their iPhone, or demand it with a court order (where I assume they can plead the 5th), but either would tip the suspect off. So they have to do it without the user's knowledge. And the only way to do that is if the company has a backdoor, or makes it so incredibly insecure as to no longer guarantee privacy at all.
The only logical way to give the FBI what it wants is to compromise user privacy.
> During the session, Comey also made repeat plays for expanding the scope of national security letters (NSL) — arguing that these administrative subpoenas were always intended to be able to acquire information from internet companies, not just from telcos.
The FBI claims that they would always get permission from a judge for invading user privacy. In the next breath, they want to expand NSLs, which is invading user privacy without requiring a judge's approval.
Both Lavabit and Silent Circle have had to close down their businesses after Lavabit was unreasonably demanded by the government (in a gag-ordered search warrant) to give up its private TLS keys, exposing all its users' privacy. But no law enforcement agency gives a shit about privacy; only secrecy.