As for don't care, sure, but I guess you can make that argument for almost anything security or privacy related. Do most people care if an app or website uses SSL? Nope. They probably can't even tell. Sometimes it's just up to the people building the infrastructure to plan ahead a bit, see what problems can arise and take countermeasures.
I think it's much easier to make progress on audited builds than e.g. PGP style end-to-end encryption. Audited builds and remote attestations are the sort of thing that can be done behind the scenes, they don't inconvenience end users. People who care can double-check what the auditors are saying, and "people who care" might include journalists, politicians and other people with powerful megaphones who can affect change.
Plus it doesn't require a big breakthrough in tech. It does require Facebook (and Apple etc) to accept that just asserting their products are encrypted isn't really achieving anything, and for some engineers to say "OK, let's find a few foreign companies to cross-sign with us". It might require some changes in the app stores. I see a post elsewhere claiming that Google is phasing out the model in which developers sign their own APKs, which is a pity and a retrograde step. But if the right people agree with these arguments, all those problems are solvable.
There is plenty of progress to be made here without getting into the next layer of how do you trust your OS. Android is at any rate in a decent place because so many users don't get their OS bits from Google but rather, an intermediary, and it's very easy to change those intermediaries (it means buying a new phone but people do that all the time anyway).
Reproducible builds and audits are all very theoretical today. Reproducible builds on their own aren't actually useful because you're just comparing hashes: someone has to have actually read the source code, understood it, documented what it does or compared it to some natural language description, and they have to keep up with all the code changes, and they have to convince other people to trust their judgement. It's a lot of work and we don't have any companies that do this sort of thing today. The industry needs a network of auditing firms that specialize in this but it's a chicken-and-egg problem: there's no point creating such a firm when their outputs are so hard to use, and there's no point making their outputs easier to use when there are no auditors who would create them.