We can learn one important thing here - it is not possible to trust closed source software. Enough said, next issue please.
On desktop and servers, however, it certainly is possible (and not-too-impractical) to verify binary blobs against known PGP signatures. See Debian's reproducible builds, for instance.
Software being closed source doesn't make it impervious to analysis. Software being open source does not mean it has been analyzed.
I don't ever want to change the tires on my car, but I think it's essential that I have the ability to change the tires on my car.
What do you think Iran/the NSA/any TLA is more upset about, WhatsApp using the Signal protocol, or Matrix and Riot?