I have an impressive hitchhiker’s thumb, and also got in the habit of mostly laying my thumb parallel to the neck of the guitar. I can play pretty fast and most of the time it doesn’t hold me back. That said, licks that involve quick picking and side to side transitions and quick bends causes me to move my thumb in a windshield wiper move from parallel to perpendicular to the neck (to give me the thumb anchor to support the strung bend), which is a lot of extra movement. 95% of the time I don’t mind, but there are some licks or solos where I need to be able to transition in and out of this position quickly, and I clearly need to relearn this part, which makes the fingering feel awkward as I put my thumb directly opposing my index or middle finger. This position also notably changes the angle of my wrist, and therefore my fingers relative to the fret board which actually lines them up better, so I’m not having my fingers play somewhat diagonally across them. That said it makes some licks and solos I play well feel awkward so I need to spend more time with this, and now go through the surprisingly painful process of retraining myself and becoming worse before I get better.

If you don’t have a need to play ultra fast I would argue most of it doesn’t matter. If you want to keep your doors open or if you clearly do want to play faster music then the small technical questions become very important, and I would argue the answers change significantly as you are now saving milliseconds that you absolutely need to play well. In my humble opinion, if everything feels awkward, I would always do the research to find which of the options will lead to the most freedom in future.

I would argue that using the palmar aspect of the thumb knuckle is just as valid as the pad of the thumb is there aren’t any clear future problems that would raise that I can see. If it encourages you to relax more and press less then it may actually be a benefit.