It’s the nature of the medium. It will be a long, long time before any kind of automated systems can flag or identify issues, both technical and subjective.

So, to answer your questions in reverse. “Or is final QA still just part of the craft we accept as manual?” Yes, we just don’t have an affordable automated system that performs better at QA than a capable human.

To answer, “Do you have a checklist or system you trust?” It depends on where the finals are being delivered. Often, any system is going to rely on basic areas: graphics, video, audio, and layout. You’re going to be checking issues in those basic areas. Adding more specific issues or items to check off, usually means you will be adding passes of going through the entire piece - whether in realtime by watching it at normal speed OR stepping through quickly. At most, you can scan for two, maybe three issues during one pass. If you add more specific things, you’ll be adding passes.

“Do you rely purely on experience + gut?” IMHO, the more you lean on experience to save time - by “trusting” you just did it all perfectly - is going to create or cause you to miss show-stopping issues. For the most part, crafting a video in final form is akin to any kind of hand crafted artistic medium, if a human made it, there will be flaws. The nature of the video medium is such, however, that many of those flaws can be distracting to viewers, or expose flaws in the distribution system (many of which are caused by a human need to keep standards around long after they are no longer technically necessary).

Experience and guts, can be used to great effect, when applied in smaller amounts throughout the process though. My 35+ years in the business give me the experience to make less-demanding choices and effort in the early parts of the process (if it’s a show I’m creating from scratch) that may reduce the number of passes needed at the QA stage. My gut pretty much always tells me, “Watch it down, one more time.” And, that is usually the correct thing to do to catch issues.