Is there a way to replace Finder altogether? It seems that a rather large group of Mac users considers Finder to be a product that contains a number of conceptual failures and oversimplifications.

It is however not clear whether Finder can be completely replaced with other application.

Is it possible to remove it from the OS, including thing like file open dialogs etc?
There's an Apple-documented general overview of the technologies that specifically support kiosk on OS X — 

Technical Note TN2062: Creating Kiosks

— with a section Replacing the Finder. 


  … Is it possible to remove it from the OS, 


I recommend not attempting to remove Finder. 


  including thing like file open dialogs etc? …


Of possible interest, in Apple Support Communities: 


preferring to not show the sidebar in expanded save dialogues