On the other hand, if iOS were open source / the iPhone was able to run unsigned code there would be nothing stopping the FBI from just doing what they've asked apple to do themselves (assuming it's actually technically possible).

Open source doesn't preclude securing the boot chain. TianoCore implements UEFI Secure Boot, and it's BSD licensed. I think the bigger issue is the (unreasonably) low trust in things like secure elements and TPMs in open source, but that needs to change, and is rapidly off topic.

More on topic is whether Apple or even Google get out from under this if their on disk encryption mechanism is open source. If everyone owns e.g. LUKS (in a sense no one company owns/controls it) then can any one company be burdened by a court to effectively break everyone else's software by being told to create a backdoor?

In that case the FBI don't get a warrant and compel a company to comply, they put out an RFP and pay a contract company to comply.