Question:

Why doesn't a Vault Object Page Layout have an option to delete a section?

Answer:

When editing a Page Layout, a section can be deleted from the layout by clicking on the Delete (x) icon in the upper right-hand corner of the section's box. 

However, if no 'x' is visible, it may be because the section is being reference in an active Page Layout Rule, and this reference is preventing the section from being deleted.  In order to make the 'x' visible and delete the section, the Page Layout Rule needs to be made inactive or deleted.  If made inactive, then the layout rule can be made active again after the section is deleted.  

Related Documentation:

Vault Help Documentation: Configuring Object Page Layouts