Yes, there you have a mesh not even approximately following the principal curvature directions.
Even with adding smoothing/fairing/proximity goals it won’t be possible to make it planar without changing the starting mesh.
From the complexity of the shape, it looks like an appropriate mesh topology will also need some irregular vertices at key points. The boundary also has some sharp discontinuities, and does not follow the surface curvature directions, so it likely isn’t possible to have the mesh grid directions aligned with the boundary everywhere.
There isn’t really any totally automated way to create this starting mesh topology. It is possible with a bit of work and skill, by looking at the curvature, maybe modelling some base mesh informed by this and/or pulling it onto the surface while letting parts slide past the edges. I can give a bit more of a guide to this process, but it’s not a one-click solution.
However, an alternative I generally recommend wherever possible is instead of getting some shape as a surface or mesh (with topology unrelated to curvature) designed in some separate way, and then trying to fit planar panels onto it in a post-rationalization process, instead embed the constraints such as panel planarity right into the start of the design process, so that you create a shape which has those properties from the start.