Good news! This was driving me crazy as well, but I accidentally discovered a couple of weeks ago that pushing the “back” button on my remote (as if I’m backing out of the show to the P+ menu) makes the “skip intro” button disappear. Same with any “skip recap” buttons. I have a Sony T.V., so hopefully this works on any smart t.v.
Alternately, we were previously subscribing to P+ through Apple TV on our Xbox, and I found that when watching Star Trek that way, the “skip” button naturally disappears after a few seconds.
rocketdave, I’m sure you are far from the only person bothered by this. I too love getting immersed in the title sequence, and found it a total nuisance. Hope this helps!