If background jobs need to be available while some other core application is down, that needs to be designed for, and that design can be achieved with any queue technology. Simply separate the queue system stack from the core application system stack.
> But if you're using Postgres as your queuing system because you're already using it as your core database technology
Note your own use of "database technology" and not "database server". It's common to have separate application and queue database servers when such an architectural constraint is present. Of course, this sacrifices the benefit of transactional guarantees when the application and background jobs run on the same server.
Like I said in the post, technology (and architectural) choices are tradeoffs all the way down :)