Over many years, checklists have been developed to try to prevent us from missing certain vital items before we carry out a maneouvre dependant on those itemse.g. Flaps and trimmers set prior to Take-Off, etc.
Most follow the same direction or order as your previously mentioned 'flow-pattern' and are logical and well thought out.
Sadly, some Ops directors/Chief Pilots/Training Captains can't help but change things when they get the job.
Hence we have checklists that mention Generators, followed by Flap settings, followed by pressurisaton checks. A complete hash and only there to satisfy the inflated ego of the man who changed it in the first place.
These men have no place in the safe conduct of aviation but sadly they are everywhere in positions of authority!
Heaven preserve us from them.