Mike, normally it is best to progress through different grits, getting finer each time. However, when preparing wood for some type of finish, you need to be careful you do not burnish the wood. That sort of burnishing, while making the wood very smooth, can also frustrate certain finishes.
Hardly any of my custom cabinet clients want us to do the final finishing. We are a wholesale shop, so our clients are installers and designers, all with established relationships with finishers.
So, we always ask for exact instructions as to how fine they want us to sand.
Since we usually are using exotic woods for doors, frames and drawer fronts, commonly the first finish to be applied will be some kind of stain. Therefore we are asked to end our sanding at 120 grit. This keeps the pores of the wood receptive to the stain. Once that stain has dried then the finisher will use finer abrasives, often starting with 150 grit.
When I have done the finishing personally I like to apply stain at the 120 grit stage. and then follow with 150 followed by 180 grit. At that point I would apply a clear finish, lightly sanding between coats with progressively finer grits.
As several others have said, cabinet doors, frames and drawer fronts are not all about round sanders. With raised panel doors there will be aspects needing in-line sanding to prepare for finishing. We own several Festool Duplex LS 130 EQ sanders. Those accept custom pads. We have made such pads for our frequently used profiles for the sticks and the edges of the raised panels. Generally the cope does not benefit from finish sanding. All this assumes the router bits are sharp. It is worthwhile to practice enough using the router to reduce the need to finish sanding those parts, since ususally raised panel doors look best when the various edges of the profile are really crisp.