It's hard for me to express how much I value one-on-ones, but I'll give it a go. It would be the last meeting I scratched if I were asked to remove all but one. I've even left a company once with the lack of one-on-ones, and their reluctance to implement them, being the primary reason. In my opinion, it was leading to numerous recurring, yet preventable, problems. A process-oriented meeting like the one-on-one would have been perfect for solving that.
So if they are truly so valuable, then why don’t more companies or managers do them? The excuse usually goes something like this: "One-on-ones take a lot of time, so we don't do them on a regular basis, but my door is always open."
"One-on-ones take a lot of time"
They do take up quite a bit of time, but it’s well-invested time that provides a long-lasting return on investment. Knowledge work is about both efficiency and effectiveness. A one-on-one of just 60 minutes can improve both that efficiency and effectiveness of a team member for the coming weeks. From that perspective, it's one of the most high-output meetings you can have.
One goal of the meeting is to address any existing or potential problems, which I’ll discuss a bit more below. Another is that to provide an opportunity for coaching. During the meeting, direct reports can get feedback on their performance, which will help them grow and reach their potential. Likewise, the manager can collect feedback on the processes, new ideas, their own performance, etc.
"My door is always open"
One-on-ones are intended to lower the barrier to discussing problems. You want issues to reach you early, so they can be addressed at a low-value stage and don't get a chance to grow into big monster catastrophes.
By saying "my door is always open," you are attaining the exact opposite goal. Now, people will have to convince themselves that the problem is big enough to be discussed first. Usually, this will prevent them from talking to their manager, even though their feedback was probably valuable. On top of that, whenever they do see someone talking to a manager one-on-one, they'll think that something is wrong. They'll also assume that their colleagues will find it suspicious if they are talking one-on-one with their manager and now have yet another reason to not talk. Compare that with, for example, a bi-weekly one-on-one. Now, there's a regular process for discussing any potential problems and there's no suspicion from others.
If done well, the one-on-one creates a safe environment where problems get tackled quickly. In good companies and teams, problems surface quickly so they can also be solved faster.