> But in most cases when I asked managers about the reason behind the deadline, the answer was something like "oh,I promised this team/director we'll do it by then". When I dug deeper to see what happens if we miss the deadline, it appeared the said team would be just fine, there were no real life consequences, just that they wanted to finish their part of work by certain time, and they depended on us.

That sounds like evidence for deadlines not being pointless.

Someone, somewhere, depended on a certain ETA. That's a deadline, regardless whether you think that there are no consequences for missing it.