I think build reproducibility is a cargo cult. The website says reproducibility can reduce the risk of developers being threatened or bribed to backdoor their software, but that is just ridiculous. Developers have a perfect method for making their own software malicious: bugdoors. A bugdoor (bug + backdoor) is a deliberately introduced "vulnerability" that the vendor can "exploit" when they want backdoor access. If the bug is ever discovered you simply issue a patch and say it was a mistake, it's perfectly deniable. It's not unusual for major vendors to patch critical vulnerabilities every month, there is zero penalty for doing this.
The existence of bugdoors means you have to trust the vendor who provided the source code, there is no way around this.
You have to trust the developer, but in theory, reproducible builds could be used to convince yourself their build server hasn't been hacked. This isn't really necessary or useful, you can already produce a trustworthy binary by just building the source code yourself. You still have to trust the vendor to keep hackers off everything else though!
Okay, but building software is tedious, and for some reason you are particularly concerned about build servers being hacked. Perhaps you will nominate a dozen different organization that will all build the code, and make this a consensus system. If they all agree, then you can be sure enough the binaries were built with a trustworthy toolchain. A modest improvement in theory, but that introduces a whole bunch of new crazy problems.
You can't just pick one or two consensus servers, because then an attacker can stop you getting updates by compromising any one of them. You will have to do something like choose a lot of servers, and only require 51% to agree.
Now, imagine a contentious update like a adopting a cryptocurrency fork, or switching to systemd (haha). If the server operators rebel, they can effectively veto a change the vendor wants to make. Perhaps vendors will implement a killswitch that allows them to have the final say, or perhaps they operate all the consensus build servers themselves.
The problem is now you've either just replaced build servers with killswitches, or just replicated the same potentially-compromised buildserver.
I wrote a blog post about this a while ago, although I should update it at some point.
https://blog.cmpxchg8b.com/2020/07/you-dont-need-reproducibl...