Center is to Approach in the same way that Approach is to Tower. You can’t go a minute without Approach as Tower when it’s busy. You technically can, ask this controller, but it can be incredibly difficult. I will argue that the same can be said for Approach needing Center, just as much.
With the addition of STARs into Infinite Flight came more and less complexity. It’s less complex because everything is automated. No more crazy “S” shapes or Doors, people are just following their flight plan and you’re making small adjustments to deconflict. It’s now simpler and more natural. It’s complex though because it may seem like you have less options.
Think of a STAR like a runway. There may or may not be that many, and all the aircraft will eventually need to funnel into one area. It’s hard to judge spacing and be proactive all by yourself as Approach, like it’s just as difficult to be Tower without Approach.
That’s where Center comes in. Center’s job is to, one, make Approach’s life incredibly easy, and two, make them look good. You wouldn’t hand Approach a problem as Center just like you wouldn’t hand Tower a problem as Approach. In order for the flow to run smoothly you need a middle man when it’s busy, that middle man being Center.
If Center is efficiently creating spacing by making small adjustments, anticipating conflicts well in advance, speeding down or up aircraft when appropriate, holding aircraft if necessary, and making sure everyone has the correct procedures inputed; then the whole airport will run smoothly top to bottom. Center is kind of like controlling departure, but the pilots never leave and you get to do other cool things.
Center needs Approach, Approach needs Center, Approach needs Tower, Tower needs Approach, and Ground needs to use all availble runways as to not annoy Center, Approach, and Tower. We all need the ATIS controller.
It may not seem like Center is vital to the flow of an airport, but it is and you won’t know it is until you try controlling with both Approach and Center open. It flows better, Approach is basically just sitting there looking pretty and clearing aircraft, and it’s more organized.