Sure, there is some noise; papers get rejected where they should not have been. And other papers that should have been rejected, do get in, etc. However, by the time you're applying for a professorship, you're abilities should clearly shine through that noise.
I'm not intending this as an indictment against academia. They're faced with a hard problem: many more candidates than job openings. They couldn't possibly do whiteboard interviews like in software, just because of sheer logistics. I don't know how academia could do it differently. Software can do it better because there's a LOT more money in software.
Being smart and knowing your areas are only some of the requirements for being a professor. Having just those two is insufficient.
If you look at the batch of assistant professors that start every year at good schools, did they pick the wrong people?
There's no implication that the letters are obtained unfairly, but that doesn't necessarily mean that the resulting outcomes are fair. The point is that if you find yourself in a situation where you can't get hold of these things and yet you are, in fact, really good, there's nothing much you can do about it short of waiting a few more years and hoping to build up a better professional reputation. In contrast, you can just show up at a coding interview, demonstrate that you can in fact code (at whatever level is required), and land a job.
Case in point: I moved from academia to coding by doing this (without any relevant qualifications or having worked professionally as a software engineer). There is no equivalent progression for someone who wants to move to academia from coding.
Prestigious invited talks don't come out of the blue, but usually as a result of consistent work that people care about.
If a researcher can't get their papers published, in an activity where that is a key metric of success and the key communication medium, what's the basis of the 'really good' assessment?
Look at the list of keynote speakers at any major conference you understand. Are those the wrong speakers? Did they get this privilege unfairly?
Every job application process has its own kinds of luck and failure modes. The time scales of academia lead to very different distortions than those in software engineering.
I don't understand your rhetorical questions. Clearly, yes, conferences choose bad speakers sometimes.
I readily agree these selection processes are not perfect, and institutional nepotism in particular is an issue in academia.
You can get a coding job just by acing a coding interview (and having basic social/professional skills). So this part of your comment did appear to suggest that merely publishing papers can be sufficient to obtain an academic position.
What possible reason would I have to interview someone if they had neither relevant experience, nor a degree? Should I just ask random people I see on the street to come in for an interview?
If you're talking about people who have no experience in the sense that they've never written a line of code, then no, obviously not. But professional experience and relevant qualifications are not necessary.
As with any job application, you need to have something going for you. It just doesn't have to be any of those two things.