Wood's grain other than something like qtr sawn cedar or redwood is not balanced enough to do the rip 5 1/4" in two stiles theory.
You need to make parts straight and flat. Then remove as little material as possible for profile or decoration.
The relationship between thickness and width can become very important with different species and sizes. A tabletop that is 1 1/2" will be more stable than 3/4" over 36" width.
Likewise a 3/4" x 24" wide panel will be more stable than a 3/8" x 24" wide panel.
24" solid wood cabinet door panel can be asking for trouble. The panel could grow or shrink in width by 1/4". 1/8" per 12" is the ballpark figure used for panels.
The flip every board idea is generally ignored in most situations. I never do it. Draw what happens on a piece of paper. The panel turns into a big sine wave(snake). In the case of a table top you will see this in the end grain. The other option is glue up expecting it to cup. Then fasten it either concave or convex. (Pull the sides down or the middle).
When making door panels we match for face grain. Ignoring what the end grain tells us. If we mill all the parts dead flat/straight, then they should stay very flat, unless they are unstable.
One thing that comes to mind is leaving a panel on a work bench overnight. Its just like throwing them on the lawn. They cup due to humidity difference.