Since OO, there is "Clear formatting" in "Apply Style" toolbar.
It clears all formatting and as https://help.libreoffice.org/index.php?title=Common/Apply_Style says:
"To reset the selected objects to the default paragraph style, select Clear formatting".
In order to make things clear, this one should be renamed to "Clear all formatting".
Steps to Reproduce:
Choose Apply Style > "Clear formatting" and compare to Format - Clear Direct Formatting.
"Clear all formatting"
User Profile Reset:
User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:38.0) Gecko/20100101 Firefox/38.0
You are of course referring to the "Formatting" toolbar. There is no "Apply Style" toolbar.
That control is a drop list toolbox with tooltip "Set Paragraph Style" , through 5.2 release it was "Apply Paragraph Style".
The "Clear formatting" action "aClearForm" calls RID_SVXSTR_CLEARFORM  and takes its label from its definition 
However, as Cor pointed out in bug 70759, the action of this control does not clear "All" formatting, just the Paragraph style -- it does not clear any Direct formatting applied and it does not clear other Style types (i.e. Character, Page, Frame, List or Table).
Removing "direct" formatting is performed with the .uno:ResetAttributes command associated with the main menu Format -> Clear Direct Formatting command.
The RID_SVXSTR_CLEARFORM action will set/reset the *paragraph* style--it should probably be to Default but as in bug 70759 it sets to Text Body.
Its labeling controlled from  could be changed, but it can not be considered "All" as currently implemented, simply see no need to change it.
As to refactoring the RID_SVXSTR_CLEARFORM to affect both paragrah style, other styles and any direct formatting--that would be more than a trivial effort.