I was always under the impression that it put the spine in an unnatural position.
No. It’s a normal standing position, with at most a very slight forward lean.
From what I gathered, those against it say it causes too many rotator cuff problems
Without agreeing or disagreeing, if this is a concern then the behind the neck push press is the answer. The drive from the legs in the push press takes the load off the rotators in the critical position in question.
and that there’s no improvement in muscle recruitment doing presses from behind the neck.
Motor recruitment is not why we do a behind the neck press or push press. We put the bar there because it’s a position that’s easier for the lifter to start the bar directly over the center of gravity without having to worry about the shoulder/wrist/elbow positioning issues of the normal press.
Personally, I don’t prescribe the clean-grip BTN press. Only the regular press or push press from the front, or the BTN clean-grip push press or the BTN snatch-grip press.