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Was it always like this?
Not exactly, no. The first game didn't really have this problem because much less was climbable (and, as I recall, you had to hit an extra button to start climbing or you'd just be running up against a wall). In the Ezio series there was more to climb but you could move quickly without free-running, which is the state where you're seeing this problem. You had to hold down two buttons for full free-running. In AC 3 they simplified it to just the one button and you had to learn to be more careful or find yourself hanging uselessly from a wall you just meant to run past. Black Flag only made minor changes to the aC 3 gameplay. Unity added more control again and so on and so on.
Because they kept making minor or major changes to the mechanics with each new game in the series, even veteran AC fans usually need to take a little time to adjust to each new game so they don't spend time hanging from walls while their objective vanishes into the distance or the timer ticks down. So even I don't know to what extent I'm agreeing or disagreeing with @sumo .
That said, if you're unable to drop from the position you ended up in, you either climbed to a position where there's no safe route down (in which case really mashing the drop button or doing a wall eject will get you free quickly although possibly into more trouble) or you encountered a bug.
Don't ask two AC fans which game had the best parkour controls. You'll hear at least three answers and start a fight.
Picked up Assassins Creed Black Flag on the PS5, after an hour I gave up the controls just drove me nuts. Run in a straight line then for some reason I'm climbing a wall, from which no matter how much smashing of buttons doesn't get me down from the wall.
Was it always like this?