A warrant alone, very likely not. A court order from a judge (slightly different than a warrant), possibly not nut it's not exactly a well tread area of legislation/law. It would probably run afoul of the first amendment given some readings, but it would have to be tested in court and would likely be argued that requiring a backdoor via some law doesn't cause compelled speech or that making that backdoor isn't protected speech etc. It's a relatively new area to be explored.

Yes. Lavabit. Those warrants demanded that Lavabit alter its system to capture passwords and/or decrypt stored email. Lavbit instead decided to stop operating and delete everything rather than comply. Such warrants have not been fully tested in courts but they do exist.

IIRC they gave up the information AND they shut down

They handed over a hard copy of their private key, a printout. The FBI went to court to demand a machine-readable copy. Then they shut down.

Thanks for that! Didn't know.

Have they been served a warrant?

Just because someone could force you to do something you don't want to do is not really a major concern if you choose, preemptively, to do the thing. The concerning part here is Apple signalling that they have executives that don't see phone scanning as a problem. That is a major black eye for their branding.

Apple's warrant canary disappeared in 2014.

The law gets debatable here. The warrant can ultimately be served only to the owner/responsible party for the system. If apple decides that they own all iPhones, a claim they've loosely made for a long time re Flash etc. Then they could be served a warrant on the device.

If they just sold the device to someone, then the police would have to issue a warrant to that individual. My understanding is that as an individual your options are either to comply with the warrant or commit a separate crime destroying the evidence or refusing the warrant.

Apple does not claim they own all iPhones.

The legal principle is the same, actually. The law says you can install whatever software you want on an iPhone and Apple cannot stop you (jailbreaking is legal). But the law cannot force Apple to make it easy for you to do so.

I haven't kept us with the latest cases, but I'm not sure where it falls on app-based SaaS.

I.e. If I use an app, on a system in which app updates are possible, which encrypts my data locally and stores it on their cloud, then the owner/responsible party for the app is...?