As someone squarely in this position for the last few years (from a prior senior engineering position), I would say my job is to try to emulate the decisions and guidance
my manager would give, but to more people than he has time to do it for.
This is fairly obvious because for a while he was doing that for too many people because we couldn't find a person for the position. If I can speed up answers and feedback and provide direction quickly in a way that's similar to what he would have do for people that often ended up waiting for him because his schedule was too busy, then I'm doing at least one part of my job well.
The more layers of this there are the more likely the message might be garbled by that game of telephone, but ultimately people can only handle so many relationships successfully, especially when they require specific regular action, and delegation (which is all middle management is essentially) is one approach that's been found to work around this.
When I'm doing my job well, the people I manage have clear directions and expectations, and if the company is managed well those expectations are seen as achievable by all involved, and if they aren't it's my job to communicate that either up or down the structure. I don't think it's sane to assume that will just naturally occur once a workforce gets big enough, so something is needed to help that along, and managers are one way to do so.