There are many, many types of software engineering roles. Perhaps you are just applying to the wrong ones. Maybe you're not a good programmer? I can't say. But even if you aren't, that doesn't mean you can't be a good engineer. You mentioned sysadmin experience, so perhaps you could focus on a DevOps or SRE role?
DevOps and SRE will still challenge you with bullshit algorithm questions at most companies, and the ones that ask for practical questions based on what you'll actually be doing on the job rather than standard algorithm or trivia questions are few and far between.
Can confirm. 50% of the roles I've interviewed for are DevOps, and they definitely ask algorithms questions. Granted, I don't think DevOps is very different from product engineering these days. It's still code.
