The behavior you have observed is by design. Please note that only a Sitefinity element can be the container for the widgets you've dropped on your page/template.
In other words, if you have a masterpage(Base), and create a Sitefinity template (SFBaseTemplate) based on that masterpage the template will display the masterpage(Base) contents, but if you drop any widgets on that Sitefinity template(SFBaseTemplate), and create another Sitefinity template(SFChildTemplate) based on that masterpage(Base) (or on a masterpage based on this masterpage(ChildMasterPage) then the widgets placed on SFBaseTemplate will not be shared with SFChildTemplate or ChildMasterPage.
In the same manner as masterpages can be based on another masterpage, a Sitefinity template can be based on another Sitefintiy template.
If we take the above example, if you base SFChildTemplate on SFBaseTemplate, then SFChildTemplate will have all the content form the Base masterpage, on which SFBaseTemplate is based andalso the content from SFBaseTemplate as it's based on that template.
All the best,
the Telerik team
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